My new bicycle skids laterally, especially in the wet; what can I do about it? My new bicycle is a new regular road bicycle (not specialist) with puncture tough tyres. The bicycle is fine otherwise but a bit rough on all the crappy pedestrian path elements in Japan like kerbs. The pedestrian path is all bitumen with various levels of embedded gravel.

It is not a braking problem- it doesn't skid forward. Turning at speed and manoeuvring (probably on a metal culvert) makes it skid sideways when wet and much less often in dry conditions. It is just a scary problem but seemingly not dangerous. 

I have bad joints and back. When I put the old bicycle to the right height for effective riding, it hurts my lower back so I don't think changing my form is sensible. 

Can I modify the bike to reduce or eliminate this problem?
After looking at your pictures, reading the description of the roads you ride on and looking at the comments here are my suggestions:

Riding Style
Change your riding style based on the surface you are riding on.

For normal cycling on surfaces with good traction a rider will lean into a turn. When the surface you are riding on is less than optimal you need to adopt riding tactics to prevent falling.


Choose your path. Bike tires are skinny, make sure they are on the best and safest part of the path. Notice the road condition in front of you. If you see loose sand/gravel/dirt is in your line of travel seek to safely avoid it. Pay particular attention to the condition of the road when making turns. If possible make turns on the dry gravel/sand/dirt free part of the path.
On gravel / sand / lose dirt change your riding style so that you don't lean into turns. Reduce your speed and rely on turning the handlebars to make the turn.
If there is wet metal in your path seek a safe way around it. Wet metal is very slick. If you have to ride on wet metal reduce your speed and avoid leaning.
If you are on dry, dirt/sand free pavement ride normally.


The key is to be aware of your riding conditions and adjust your riding style to stay safe.

Tires
It might be possible to find a tire that will improve your traction on gravel or adjust the air pressure in your current tires. There are three tire characteristics that improve traction on gravel:


Tire width - Off road bikes have very wide tires to help with challenging traction issues. You won't get much - if any - wider tires on your bike so this won't help much. The good news is that your tires are not super skinny now.
More aggressive tread. You might be able to find a tire that fits your bike designed to get more traction on gravel/sand/dirt. It would be good to have a conversation with someone at your local bike shop on what is available.
Tire pressure. Every tire has a maximum rating that works well for good traction situations. You can experiment with different tire pressures and see if a lower than maximum rating pressure helps. Try running the tires 3 PSI lower than max and see if that helps. Don't get carried away with reducing tire pressure. If the pressure is too low the tires can slip and tear valve stems.


Summary
I think your best solution is to adopt riding tactics that fit the road surface you are riding on. Avoid poor traction situations. When you can't avoid a poor traction situation slow down and don't lean.

If you don't have one already make sure you ride with a helmet.