Might be shorter to list what you can keep:
Frame and fork(probably, if the OLD spacing is the same)
Bars and stem
Saddle and seatpost
You will need to buy or source replacement:
Rear wheel hub because a freewheel and a cassette are too different. And its a sad truth that a whole-new wheel might be cheaper than a hub and ...
If your goal is to convert your 3 gears in the front and 7 gears in the back to a 3 in the front and 9 in the rear this will be quite expensive. A new rear wheel will be required Your current rear wheel uses a screw on freewheel to mount the rear gearset. Nine speed rear wheels use a freehub mounting system with a cassette. You will need a 9 speed rear ...
This is a partial answer.
What else you will need: a rear shifter, your Shimano ST-EF41 will not be compatible with SRAM-X9 (as far as I know).
On the other hand, SRAM and Shimano 9-spd cassette/chains should be interchangeable, so if you can (virtually) upgrade your Tourney 7-spd to something 9-spd Shimano, you should be able to then replace this something ...
There's more to front derailleur adjustment than limit screws and cable tension. Both the angle of the derailleur and the height need to be set properly.
The angle of the derailleur being off can cause chain rub against the cage. If the rear of the cage is angled too far outward, the chain can rub against the inside of the cage when the chain is on the ...
Are you trying to bring the derailleur farther outwards? If so, you need to add cable tension. Screwing out the H limit screw won’t help if there isn’t enough tension to get to the limit anyways.
To check for chainring problems, derail the chain from the chainrings entirely and give the cranks a spin. If you see the chainrings wiggle side to side, then you ...
The little riveted points you mention are pivots, there are a bunch of them. What you can do is spray a little lubricant in each pivoting part of the derailleur, then physically move it side to side by hand a number of times and it should loosen up. Pull it towards you and then push it back, 10, 20, 30 times.
It might take a bit of force to start with and ...
It can be dirty, but it can be inside the cable and not on the derailleur itself.
See solution here:
Shimano Deore front derailleur occasionally sticking
It can also be the L-screw, or the derailleur position, or even both. Check the L-SCREW ADJUSTMENT section of the ParkTool webpage.
The option I took in the end worked really rather well - I upgraded the front tyre from 2.1" to 2.25" (Nobby Nic) and kept the back at 2.1" with considerably more tread (Rapid Rob) for trail centre and winter use. Handling on mud and wet roots/rocks is much improved (at the expense of heavier going on road, but I can refit the WTB Nanos for ...
Use a side swing derailleur such as this one: https://bike.shimano.com/en-EU/product/component/alivio-m3100/FD-M3100-M.html
This eliminates the linkage behind the seat tube, giving you more clearance. It mounts via a normal band clamp. Versions are also available for E-type and direct mounts.
Some of Shimano’s pics: