[Build Ready] Building a budget gaming rig ($500~). Requesting a second opinion on if everything looks good so far.

This will be my first build. This build is a variation on /u/epicpant's build. (Linked here.

PCPartPicker part list / Price breakdown by merchant / Benchmarks

Not included is the OS, keyboard, mouse, or monitor. I have a spare HP w1907 that I can use until I save up for a decent monitor.

My budget is capped out at $550. I'm not interested in an optical drive since you can boot up windows from a thumbdrive.

A few questions:

1. Will my monitor be compatible with this build? It is a little old but it's still functional. It does not have an HDMI input, just analog.

2. Are there any incompatibilities with the parts I've listed?

3. Are there any better parts that are cheaper? (Sans RAM. I'd feel more comfortable with 8GB rather than 4GB.) Will I get good mileage with the combination of computer parts?

4. How well would this setup be able to run Battlefield 3? I'm using this game as a starting point, since it's one of the top-of-the line games in terms of graphics. I feel that if this setup can handle BF3 on medium/high settings while maintaing 60+ FPS, I'd be set for 2-4 years till I build a new rig.

Thanks in advance!