I havent torn down your title, to share specific answers, but in general, Yes, you should tear down as much as you can and are comfortable with to clean, wax, and change rubbers out.
There are high volume threads with regard to cleaning, and waxing, along with the debates of material choices.

A good choice for all the supplies you need is Pinballlife.
You might likely wish to change your bulbs to LEDs, at the same time.

Regarding difficult cleaning, there are methods of rags on snakes, to clean hard to reach areas, on back loops, and deep levels.
Not a perfect answer, but helpful.

Regarding IJ specific tear downs, you will likely get more help if you post your question in the IJ specific threads, that have daily visits.

Good Luck!

Art

Porter - as Old Guy suggested, read thru the Indiana Jones thread.

To answer your specific questions - removing the POA is not difficult, but intimidating. There are several step by step instructions in the IJ thread. You will need to remove the ramps to replace the slingshot rubbers. (I think that's what you're referring to.)

You will need to remove the POA, ramps, ruins, and some plastics to replace all the rubber rings. If you're going to replace them, to me its an all or nothing. Before proceeding, take lots of pictures from every angle. Digital pics are cheap. Take several pictures before and after every step you do. For spacers, put a ruler on them so you can keep track of length during teardown. Take more pics than you think is necessary.

I agree with LEDs - the connectors are right at being undersized, and will burn up over time. There are several places that sell LED kits for IJ, or you can go it alone. If you go it alone, I suggest a cruise thru the thread of No Rainbow puke club so you can get an idea of what the different colors are.

For the middle drop targets, keep in mind the middle drop is thicker than the outer ones. If they're not broke, maybe new stickers on the faces will give you the look you need. Again, the IJ thread has links.

One other thing - and this is very scary - you mentioned the family has had the machine for fifteen years. Are the batteries fresh? Any signs of leakage? While in there, take a look at the connectors on the bottom of the largest board to see if any of them are starting to burn. This is the first point of failure for the light circuits. If not sure, post several pics - someone will chime in.

Welcome to Pinside, and you can learn to do this.

I would clean what you can reach, INCLUDING the subways *very important(plastic tunnels the ball travels thru, underneath the PF), but I wouldn't go whole hog. If you can, break the PF up into pieces and deep clean one at a time. If you're new to it you probably don;t want to take everything off the machine and be left with 100s of pieces that need to go back together a certain way.

IJ is one of the easier games to tear down. Take pictures and go slow, you will be fine. It will be dirty in a few days if you don't clean under the POA, the subways and the loop that is blocked by the ramps/POA. Make sure you identify and disconnect everything under the playfield (switches/flashers on the ramps, POA connectors) before you start taking things off the top.

When people say "read through the Indiana Jones thread," THIS is the post they're talking about:
https://pinside.com/pinball/forum/topic/ij-williams-you-cheat-dr-jones-club

Here's where you want to ask for help with this specific game. There's a lot of good info already there, but more importantly these are the people who know the ins and outs of this machine.