(1) Je lui ai tenu fermement les hanches

Your strategy for understanding tenir is a good start, but you shouldn’t combine two definitions where one takes a direct object and the other an indirect object. Instead, if the verb can take both at once, you’ll find an entry that shows both.

For example, here’s a WordReference subheading for donner that accounts for each object in this complex-looking set simultaneously:

So why does your tenir have both a direct and an indirect object if there’s no subheading tenir [qqch] à [qqn] ? Answer: lui identifies the owner of the hanches. This would be hard to interpret until you know this pattern: Body parts can be connected to their owner by an indirect object.

This might sound somewhat absurd, but you’ll recognize it from familiar phrases like these:

Je me lave les mains.

Tu te brosses les dents.

Anglophones are tempted to say « Je lave mes mains » and « Tu brosses tes dents ».

So the phrase you quoted is like « J’ai tenu fermement ses hanches » (if you could say that).

Generally, French conceptualizes body parts oddly. It seems to avoid possessive + body part as often as possible. For example, one doesn’t say « Ma tête tourne » but « J’ai la tête qui tourne ».

(2–3) il prenait vraiment son pied

You were right to suspect that this odd-sounding position is due to its being an idiom. I’m not sure why your search on WordReference failed to turn one up. Here’s the entry:

have a blast, have a great time, have a ball

I switched the language to French-English and watched for new suggestions as I typed each letter.