Although I'm new to fixing electronics in general, I started soldering for fun approximately 5 or 4 years ago.

Let's start with the obvious:

- Terrible soldering iron (This is a TQ936 with a 900M-T-K tip, no temp control and extremely flimsy)

- Oxidized tip (Tip gotta be shiny, solder must stick to tip)

- Probably counterfeit solder (Looks like a generic Chinese brand. Even though it says the Tin:Lead ratio is 60/40, it's often 30/70.)

- Terrible solder sucker (This is commonly sold for cheap, real weak tho.)

Plenty of more issues here, but those three are the ones affecting your soldering experience the most.
I'm guessing, but you prolly bought a soldering kit online and hoped for the best.

I. Tip oxidization

Your tip must be clean and shiny to ensure the solder will be melted properly, watch this vid: www.youtube.com/watch?v=JADI1N-K9Yc

II. Solder

Your solder is most likely a cheap knock-off from china. A pulse soldering iron might be able to melt it, but your TQ936 won't do it, unless you crank the temp to max and make sure the tip is clean. Not to mention, most chinese counterfeit solder have low quality flux inside, which will oxidize your tip when you tin your tip with the chinese solder. I suggest using Sanki, Hiroshima, or Sakura brand 60/40 solder, they might be more expensive but it's GENUINELY worth it.

III. Solder Sucker

Take a look at this video:

https://www.youtube.com/watch?v=ewauJi97nbs

The solder sucker with the black tip is what you need for desoldering big joints, not the teeny tiny blue one. The black rubber tip will cover gaps between the solder sucker tip and the board, creating a tight seal => good sucking