Order of priority for including functional groups in the parent chain compared to order of priority for numbering the parent chain The following is about the IUPAC naming system.

So as far as I understand the rules for numbering a chain are as follows:
Compare the locants of functional group 1 in both cases if the are lower in one of them it wins. Compare the locants of functional group 2 in both cases if the are lower in one of them it wins. And so on for all functional groups in order of priority. And then in the end we compare the locants for all substituents in alphabetical order.

But the rules for choosing a parent chain are the same, except we firstly want to maximize its length and after that we want to maximize the number of functional group 1s, functional group 2s and so on. And after that we want to minimize the locants for functional group 1, functional group 2 and so on until any of them is better. I am not sure what we do after that though.

My main 2 questions are the following:

Is the ordering of the functional groups the same for all 3 steps (maximizing the number of functional groups in the parent chain, picking a parent chain with minimized locants of the the functional groups, and then the same but for directing it)?

Where can I find the ordering of all functional groups or at least the following functional groups: alkyl (are alkylidenes in the same category as alkyls?), halogen, OH, double bond, triple bond, and  NO2?

And I know that sometimes two or more of these are grouped together in a set (for example double and triple bonds) so an ordered list of these is not enough.

Can you please provide something like (Set of double and triple bonds)>(double bonds)>alkyls but for all of the listed? If not where can I find such a thing?

Please tell me if any of that is wrong.
There are indeed several analogous criteria for the numbering of locants and for the choice of a principal chain; however, there are also significant differences.
The most important simplified criteria for the numbering of simple acyclic compounds are:

lower locants for suffixes
lower locants for multiple bonds
lower locants for prefixes
lower locants for substituents cited first as a prefix in the name

The most important simplified criteria for the choice of a principal chain are:

greater number of suffixes
longest chain
greater number of multiple bonds
lower locants for suffixes
lower locants for multiple bonds
greater number of prefixes
lower locants for prefixes
lower locants for substituents cited first as a prefix in the name

You can find the corresponding actual wording of the nomenclature rules (taken from Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book)) below. However, the IUPAC recommendations have more than 1500 pages. Hence, you should be careful when applying any simplified or abridged version of the nomenclature rules.
Also note that there is no order of priority for substituents cited as prefixes (e.g. ‘bromo’, ‘chloro’, ‘ethyl’, ‘methyl’, or ‘nitro’). All such prefixes are considered together as a set. However, you need the seniority order of compound classes in order to choose the senior class that is expressed as a suffix.


P-14.4 NUMBERING
When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:
(…)
(c) principal characteristic groups and free valences (suffixes);
(…)
(e) saturation/unsaturation:
  (i) low locants are given to hydro/dehydro prefixes (…) and ‘ene’ and ‘yne’ endings;
  (ii) low locants are given first to multiple bonds as a set and then to double bonds (…);
(f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;
(g) lowest locants for the substituent cited first as a prefix in the name;
(…)



P-44.1 SENIORITY ORDER FOR PARENT STRUCTURES
When there is a choice, the senior parent structure is chosen by applying the following criteria, in order, until a decision is reached. These criteria must always be applied before those applicable to rings and ring systems (see P-44.2) and to chains (see P-44.3). Then criteria applicable to both chains and rings or ring systems given in P-44.4 are considered.
P-44.1.1 The senior parent structure has the maximum number of substituents corresponding to the principal characteristic group (suffix) or senior parent hydride in accord with the seniority of classes (P-41) and the seniority of suffixes (P-43).
(…)
P-44.3.2 The principal chain has the greater number of skeletal atoms [criterion (b) in P-44.3].
(…)
P-44.4.1 If the criteria of P-44.1 through P-44.3, where applicable, do not effect a choice of a senior parent structure, the following criteria are applied successively until there are no alternatives remaining. These criteria are illustrated in P-44.4.1.1 through P-44.4.1.12.
The senior ring, ring system, or principal chain:
(a) has the greater number of multiple bonds (P-44.4.1.1);
(b) has the greater number of double bonds (P-44.4.1.2);
(…)
(h) has the lower locant for an attached group expressed as a suffix (P-44.4.1.8);
(…)
(j) has the lower locant(s) for endings or prefixes that express changes in the level of hydrogenation, i.e., for ‘ene’ and ‘yne’ endings and ‘hydro/dehydro’ prefixes (P-44.4.1.10);
(…)
P-45.2.1 The preferred IUPAC name is based on the senior parent structure that has the maximum number of substituents cited as prefixes (other than ‘hydro/dehydro’) to the parent structure.
P-45.2.2 The preferred IUPAC name is based on the senior parent structure that has the lower locant or set of locants for substituents cited as prefixes (other than ‘hydro/dehydro’) to the parent structure.
P-45.2.3 The preferred IUPAC name is based on the senior parent structure that has the lower locant or set of locants for substituents cited as prefixes to the parent structure (other than ‘hydro/dehydro’ prefixes) in their order of citation in the name.
(…)