bathroom
The bathtub was installed without a mortar bed just the foam it comes with during transportation and seemed to be fine but after few weeks it started to squeak when taking a bath.
I have access to 3 sides of the tub and thin king of adding mortar under it but I read that expanding foam and plaster could also be an option.
Any advices over which option is better? I'm not familiar with what kind of plaster to be used.
Your external list is pretty good, what's missing is an internal list:
It is unusual for these sources to end up on the floor, outside the tub, unless your bath is over a slab.
If you have access (if not, you should make one; 14" square centered on the valve) to the back of the mixing valve, use a flashlight and watch carefully when the water is first turned on, after its been off overnight
Why do you think the bathtub is not currently vented?
Not all traps need to be individually vented so you're not always going to see a vent if you don't know what to look for. It's a little hard to tell from your photos, but I think your bathtub is wet vented through the kitchen sink:
Please correct me if I've got the arraignment of your pipes wrong.
Best Answer
I have done this with plain Plaster of Paris, which I consider to be the best option - it's stable, but easily removed if/when the tub is replaced. I had planned to set the tub, pull it and place a pile of plaster, then reset it, but setting it the first time was such a chore that I did it from the other side of the wall instead.
It will be a bit messy, so prepare for that. With plaster you need to keep the relatively short working time in mind (it sets fairly quickly) and be sure to push enough in from the side you can access to support the opposite side. I ended up mixing several smaller batches so that I could get them placed before the plaster set, and filled in from the far side to the side I had access from with successive batches.