It should be noted, that for most if not all of these, the answer depends on the specific mechanics in this speculative scenario:
- How accurately can the target place and time be specified?
- Do only set locations work, or is it completely free spacetime travel?
- Are there risks and common errors, or ways in which these machines malfunction?
- What sort of time travel scenario is it? Are branches in the multiverse created each time somebody travels through time, or is it a single timeline? And if it is a single timeline, is it internally self-consistent, or can it actually break and be changed?

These and similar questions may affect how easy or possible it is to avoid running into various problems, including effects on mental health.

Additionally, there are generally two sides to consider:

a. Effects on the time traveler - Here, mitigation strategies mostly come down to picking your targets and missions carefully, and preparing for the events you are about to encounter as much as possible: Read up on as much history and as many records of the time and location as possible. Try to understand as well as possible, what you are getting into, what sorts of situations you might not be familiar with from your own time you might run into, and what to do in the case of any sort of emergency. Prefer targets that don't put you in immediate danger. And more specific to the mental health side of things, perhaps make an effort to learn mental health coping and calming strategies, and prepare with stress training to avoid panic and improve routine. Also specifically consider the medical possibilities of the target era, and take any tools or medication you might need, that is not accessible at the time, with you.

b. Effects on the lives of people and other lifeforms in and near the target spacetime location - This side of things is much more concerned with preservation: As a person from the future, you will have unique access to the power of hindsight which, in some situations, can yield to massive advantages and even the knowledge of facts some people at the time deem private, that only broke later in one way or another. It is important to respect boundaries and consent of people in such scenarios. As a result, in most time travel stories it is recommended to avoid or minimize contact, and to carefully assess what people at the time are supposed to already know and to be very careful about how to use future information. Usually this is about something abstract such as keeping the timeline intact, but it can also be about the very real harm and distress misusing information, intentionally or not, may cause, including to the psyche of contacted people.

That said, here are some general ways in which these issues could be mitigated:

1. Post-traumatic Stress Disorder (PTSD) - It should be noted, that sometimes the events that cause this disorder can seem quite mundane to others who are not affected by it. However, certain historical events, such as active war zones or natural disasters, are more likely to be cause of PTSD and should thus be avoided during time travelling where possible. It is probably also not a good idea to travel to times and locations entirely unfamiliar to you without significant preparation: Running into a live Cretaceous predator roaming prehistoric rainforests might sound fun until you very nearly land on their menu.
On the flipside, efforts should be made not to traumatize people of the past with unnecessary information. If contact is necessary, trying to fit in, or at least pass as a perhaps eccentric but otherwise non-threatening stranger from a distant land or something like that is probably a good strategy.

2. Delusional Disorder - As a time traveler, perhaps keep a journal or log with carefully kept timelines and how they cross, in order to keep track of what is or isn't real, or what has or hasn't happened yet. It is probably a good idea to do this in a buddy or group system. Keep a more constant group of people around you that keep you grounded and serve as a fixed point and reference for your experiences.
As somebody in a targeted space time location, you have little power over what a time traveler might choose to divulge to you, so it is on the time traveler to make sure they use their informational advantage responsibly and, should information accidentally flow and potentially cause delusions, offer as much support as possible to avoid or mitigate this issue. The time traveler should particularly avoid gaslighting anybody from the target space time location, in order to avoid them losing trust in their own senses and thoughts, which might fuel further delusions.

3. Dissociative Disorder - For the time traveler, the advice here is very similar to that for delusional disorder. Keep track of reality in records and keep a trusted group of people around you to ground you in reality. For a person from the target space time location, it's best to avoid brining them along to other times, such as what, to them, is the future, which could be a highly confusing and traumatic experience and cause dissociative disorder. Certainly don't do this without a serious and deep effort for informed consent. If it is really necessary for some reason, to bring somebody from the past into the future, this probably should not be done without waiving a significant part of the policies that usually would be in place: Inform them about what they will experience, what differences there are, and about all the risks associated with such a move. Only if you can make sure that they understand to the degree it is possible, may such a move seriously be considered. Be respectful of the other person's mental state at all times.

4. -  7. Depression, Anxiety Disorder, Psychotic Disorder, Substance Abuse Disorder - These issues may all be different from each other, but the way to avoid them is essentially covered by the same or very similar strategies to what has already been described. Prepare yourself as well as possible, take and review logs, keep a support network as an anchor to your sense of reality, be responsible with your future-given information and generally respect the boundaries, values, and mental state of any people in the target space time location.

8. Sleep disorders - This issue only really affects the traveler. In addition to implementing some of the previous points, it can be mitigated by precision-landing such that the source and target times happen to line up as well as possible, thereby continuing the circadian rhythm uninterrupted. It should be noted, that this is more difficult to accomplish this if the plan involves multiple time critical travel stops in, to you, relatively short succession. However, it is relatively difficult to imagine a situation where that is truly necessary, unless there are specific limitations to time travel: If it is a quite free form of time travel, you could always just spend what to you is days or even weeks of time to relax between missions that, in somebody else's frame of reference, are only minutes apart. So as long as the scenario allows it, the best way to mitigate this issue is to prepare for the sorts of times you'll have to be active during weeks or more in advance.

9. Identity Issues - Mitigating this has essentially already been covered by points 1. - 7.

10. Obsessive-compulsive disorder (OCD) - This issue is somewhat in tension with the idea of keeping and reviewing logs keep track of reality from the perspectives of both the target space time location, and your personal timeline. However, this can probably be somewhat mitigated by involving multiple people who can serve as an anchor, or pick up some of the logging responsibilities. Sharing the burden and having people to talk to about experiences is likely to help avoid or mitigate this issue.
For a person from the target space time location, it is probably best to avoid divulging information specific to cleanliness or microorganisms, in particular if this is a time before these concepts were widely understood.

Should all of these strategies not suffice, consider professional help from mental health experts, therapists, and counselors, as well as medical support when needed.
Note, however, that these services may not be available to people from some past space time location, so extra effort should be taken to avoid causing such distress in the first place.

And of course, it is important to note that, while each of these conditions do exist, the context of their occurrence here is purely speculative and hypothetical, and there is no scientific evidence that time travel is possible or, if it were, would lead to any of these conditions.
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