You can add a little baking soda to raise your alk. I'd add a couple pounds at a time slowly to the skimmer while the pump is running. After a couple hours, retest and redose until you get it somewhere between 80-125. Your pH is ok at 7.2 but you don't want it lower. We use 20 Mule Team Borax (laundry aisle at Walmart) to raise pH. You add it in the same way as the baking soda. Actually, you can add them one right after the other. I'd start with a half a box and see what that does for you. You want pH somewhere between 7.2-7.8. I usually keep mine around 7.4-7.6.

If you are going to use the trichlor pucks, you'll need to keep an eye on your pH and your CYA. They are stabilized which means they add CYA. If yours is already at 35, you can use the pucks for awhile, but when your CYA gets to around 50, you'll want to quit using them and only use bleach. You don't want your CYA too high. The trichlor pucks are also quite acidic and will push your pH down.

As far as calcium hardness is concerned, vinyl pools don't need calcium so don't worry about it.

Like Jan said, do yourself a favor and get a good kit. Test your chlorine daily, pH a couple times per week (unless you are tweaking it), alk every couple of weeks (again, unless you are tweaking it), CYA every couple of weeks until you hit 50 and then your CYA should stay pretty stable for the rest of the summer.

Hope this helps!