Max Upgrades and more questions

To start with you won't be able to use the MacBook Pro CPU as its soldered to the logic board and is not the correct carrier package to use in your system.

You'll need to buy a new CPU which given the age will be difficult to find! But before you can swap out the CPU you'll need to first update the systems firmware so the CoreDuo or Core2Duo chip is recognized.

• The best CPU you can use is either the Intel Core 2 Duo T5600 or T7200 (Merom) as your system Bus is only 667 MHz. Here's the IFIXIT guide: Mac mini Model A1176 CPU Replacement

Now the bad news...

• The maximum RAM your system can support is 3 GB which you can use 1x1GB & 1x2GB modules or 2x2GB modules but the last 1 GB won't be usable. The graphics services use the upper address lines which is why you can see the RAM in the system report but the system can't leverage it.
• Your system is limited to one 2.5" drive so while you can install a larger drive or even a SSD the limited RAM will impact the performance of your system beyond a 500 GB drive as the RAM stores the drive mapping. You also have only a SATA I (1.5 Gb/s) SATA interface so what ever drive you get needs to support this older standard, Review the drives spec sheet if it does not explicitly list SATA I support it won't work.
• As far as swapping out the logic board you are limited to the A1176 series of boards, The logic board layout is very different in the next generation (A1283) so it won't fit or work.
• The GPU logic is part of the logic board and not swappable
• You likely need to replace the fan if it's making noise your only choice is to replace it with the exact same unit: Mac mini Model A1176 Fan Replacement and here's the part: Intel Mac mini (Model A1176) Fan the bearings often wear out.
• Sorry to say this is a very limited system in upgradability due to its age. Today newer Mac Mini systems allow more RAM and storage options but even they have their limits!

Frankly, I think its time to look at saving ones pennies to but a newer model. I would look at a 2011 model like this one: Mac mini 2.7 GHz Core i7 (Mid-2011) Or at least review the different models here: Mac Mini model listing to find what you would like and what the limits are RAM wise and number of storage devices and their I/O speed.