Solder Socket Connectors To Motherboard 1) Fan & 2) Speakers

I own a Mac Book Pro 13” Mid-2010 [last model with all the good connections/plugs and CD drive]. I rather learn to “Do It Yourself” vs. pay computer technician. Invest time to earn knowledge, and spend money on tools and upgrades.

Motherboard Cannot Disconnect for Adding Thermal Paste (To Fix Overheating)

Screen connection stuck, socket connectors of Fan and Speakers ripped from motherboard.

I watched YouTube instructions how to fix overheating laptop. I purchased “thermal paste”. Instruction video showed to remove motherboard/logic board, all connections have to be disconnected (to apply thermal paste on heat sink under motherboard). Unfortunately, I ripped the socket connectors of Fan and Speakers from the motherboard. Screen cable stuck, not dare to try to disconnect. If not ad new thermal paste, will motherboard overheat, or okay if not replace thermal paste, only replace HDD with SSD drive?

Soldering Motherboard (Fan & Audio Socket Connections)

Where can I find genuine new fan replacement, reliable seller, but not overpriced? Amazon complaints of faulty/fake knockoffs.

Can I solder socket connections (fan and audio) back onto motherboard, without removing motherboard?

Use rosin wire without flux (to prevent erosion)? Or not stick well enough without flux?

Or is best option mix solder paste with flux, apply to motherboard, then solder with micro soldering iron? This strategy appears easier dosing solder vs. using solder wire.

What products do you recommend? Soldering iron, soldering gel + flux, or soldering wire (size ?) + flux. NOT lead free, lead free needs higher temperatures.

I already purchased: screwdrivers, stand with helping hand with light & magnifier, antistatic wrist band, smoke/fume extractor.

If I successfully repair motherboard connections, I will later upgrade 4 GB RAM to 8 GB RAM and HHD drive to SSD drive (less heat).