Welcome to Just Answer. I will do my best to fully answer your question(s).

The 1st thing to look at regarding the sink is to remove the aerator screen (where the water flows out of the faucet). As this could be partially clogged.

As for the tub, usually in apartments these faucets are of a "pressure-balancing" type of faucet. Translation- they need equal pressure (or close to it) on BOTH the hot and cold water supplies to work properly. If it isnt equal the cause can come from a few places.

some faucets have a "balancing spool" that can be replace along with the faucet cartridge. If that doesn't solve it the next cause is either a partially blocked water supply line (usually close to the water heater) hot supply line, but not necessarily. Or the piping supply lines may just be too small to supply sufficient supply. You mentioned he replaced some of it. 1/2" ID (5/8" OD) water lines (minimum) is required for a single fixture. If others are on the same line then it must be increased to 3/4".

I gave you alot of info to digest. and alot to look at regarding the issues. Start with removing the aerator on the lav to hopefully eliminate that one issue. If that does no good then Id start looking at a clogged water line.

Good luck as I know some landlords can be difficult when it comes to resolving tennant issues.