With regards to your first question. The hardware you specify should have no problem whatsoever in loading/running PT in the blink of an eye and at lightening speed. If you are having serious lag/delay problems, you may want to sweep your PC for Spyware and AdWare.
Two good programs to use for this are AdAware (
www.lavasoft.de, download the free personal edition) and SpyBot Search & Destroy (
http://www.safer-networking.org/en/download/).
If you install, update and run both of these programs and remove any threats they find (if you have never scanned with anything like this before, do not be surprised if you find hundreds, even thousands of infections), you should notice some improvement in performance. At the very least you will have the peace of mind that there's not a load of dodgy programs/processes running on your machine.
Second is to make sure you have a good AV (Anti-Virus) app. My weapon of choice is AVG Free Edition from GRISoft (
www.grisoft.com). It's free to download, free to update and is a good basic guard against viruses. On all of these programs, try to keep them as up to date as possible, perhaps checking for updates once a week if you use your PC 4-5 times a week, maybe every day if you use it for 5-8 hours a day. It only takes a moment to update, and keeps you (better) protected.
If none of these steps show an improvement in your basic performance, I would suggest that the problem is something deeper, possibly a hardware problem, but it is hard to say without more information. But as I say, the CPU that you say you have, combined with a GB of RAM says to me that you really shouldn't be having any lag/delay issues with running an app as simple as PT.
Now, for your second enquiry. Again, this is very hard to be precise about as you give very little information about your exact equipment and the precise nature of the problem. As I understand it, you are having small periods of time (perhaps only a few seconds or fractions of seconds?) where your net connection is not being responsive, meaning that your online activities, such as poker clients, are lagging and causing you to miss turns etc...
You don't say what speed cable connection you have, but I would imagine it must be 512k or faster, which is more than adequate for online poker without delay. Anyway, find out what speed your connection is supposed to be (it should be detailed somewhere in your signing up package or confirmation email, something like that), then go to any of the speedtest websites (for example:
http://www.bandwidthplace.com/speedtest/) and take a test there to see what speed your connection is actually performing at. If it is significantly below what it should be, you could have a problem somewhere, either with your router, modem, PC, or the configuartion of any one of these...
As I say, it is difficult to say exactly what could be causing these problems without more detailed information about your setup and configuration.