Let me see if I can clear things up for you.
The biggest reason you're having trouble is your graphics card is extremely low end. With most nVidia cards, the second digit is the most important. Yours is a 1, which is almost as low as it gets. Further, since you've got the mobile version, it's even worse. Mobile versions of graphics cards will always perform at lower speeds than their desktop counterparts, due to power and form factor restrictions.
Sorry to put this as bluntly as I'm about to, but whoever told you that ANY machine with a GeForce x1xx in it would be "good for gaming" was either a liar or a complete idiot, or possibly both. I'm curious what your friend has that he says is worse than yours. Unless you go back a good many years, you can't get much worse than what you've got, I'm sorry to have to say.
In case you're wondering, here's what the numbers (usually) mean. The first digit denotes the card's manufacturing series, and the second tells you the card's performance level within the series. In most cases, the second digit will trump the first, by a long shot. A Geforce 8800, for example, will perform better than a GeForce 9500, even though the 9500 is newer. A 7900 will perform better than an 8600, even though the 8600 is newer. Etc.
Your first digit is a 7, meaning the card is from the GeForce 7 series is now several years, and three generations, out of date. It was current back in 2005-2006, which practically makes it a dinosaur in computer years.
Your second digit is a 1. Zero is worst, 9 is best. 1, needless to say, is pretty bad on that scale. For SL, and for gaming in general, I don't recommend anything below a 6 in the second digit if the card is 8 series or below, or anything below a 5 if it's 9 series. (Performance wise, a Geforce 9500 is identical to an 8600. They offset everything by 1 with the 9 series for some reason.)
As for replacing the card, that's not something you'll be able to do. You'll have to replace the whole machine. The 7150 is an IGP (integrated graphics processor), built right into the motherboard. It cannot be removed by itself.
Changing components in laptops is usually a no-go anyway, even with parts that are not integrated, again due to power requirements and form factor. With the exception of hard drives, and sometimes RAM, it's extremely rare that you can upgrade much of anything, let alone a graphics card, in a laptop. It's not like snapping together a desktop. Laptops have almost no standards. The system designers for each model often have to bend over backwards to find ways to cram the needed components into the tiny spaces the chassis designers come up with. It's usually not a pretty picture inside.
Laptops that do feature upgradable graphics modules are extremely expensive. They usually fall under the "desktop replacement" category, are quite large in size, and cost many thousands of dollars. That inexpensive little HP you've got couldn't be further from that description.
Bottom line, if you want better performance, you'll need to invest in a new machine. I recommend ASUS or Malibal. You can find a good selection of ASUS machines at newegg.com. Malibal sells direct, via malibal.com.
(Do NOT buy an ASUS laptop from Best Buy, by the way. The ones they have there are lower performance configurations, with worse warranties, and with very restricted access to tech support. The slightly lower price tag Best Buy offers is NOT worth the sacrifice of features and service.)
Whatever you get, make absolutely sure the graphics card is up to snuff. Remember, you want at least a 6 in the second digit if it's a GeForce 8 series or below, and at least a 5 in the second digit if it's a GeForce 9 series.