Yes, you can upgrade.
Yes, you can upgrade.
The Athlon II X4 635 is supported on your motherboard. More details can be found at the provided link. However, your cooler might find it hard to manage the quad-core processor, especially with a TJmax of just 71°C. The VRMs on this board also seem subpar. Are there any "e" models available in your area, such as the X4 615e or X4 610e? These are lower-power variants that consume less energy, making it easier for your board and cooler to handle them.
Your aim is to upgrade or stabilize your setup. The 250W PSU for a 4850x2 rig seems risky because that card alone might hit its limits. Continuing like this could cause failure, likely due to the single-core limitation preventing full performance. Upgrading to a better CPU would probably be necessary, though it may not be ideal given the outdated and weak processor.
I believe that the OP was mistaken in what the graphics solution there is. The computer is clearly using on board graphics. This is OG on-board graphics, as in, on the motherboard, and in this case is from the AMD760G chipset. It's clear from the pictures that there's no card in the system, and the OP calls it "integrated graphics." My guess is that some application misidentified the graphics as an HD 4850X2 for some reason, which is plausible as both solutions are from the same era, which is quite old, so a newer program might not have programmed with accurate knowledge of what the graphics are.
Can you modify the Sempron 150 with a 2.9 GHz processor to work with an Athlon II X4 635 at 2.9 GHz?