The fermentation all depends on what yeast you used and what the starting SG was. For instance, if you use a yeast that has an alcohol tolerance of 18% and you start with a low SG like 1.085 then you will ferment to under 1.000 unless something goes wrong. If you start with a SG of 1.130 and use a yeast strain with a low tolerance of 13% then you will exceed your yeast strains ability and end up with an SG of around 1.030.
As for checking your SG in carboy, I typically check when there is no action in my airlock but i use the S-Type airlock which bubbles when active. If making a it wine then check it a few days before what it says because they typically ferments faster then what they specify. If its a fruit wine then they could go just as fast or take months. You will gt a feel for this after a little while and dont worry about oxidation as way over stressed. A little oxygen will not hurt your wine but do keep your wine topped up when done fermenting as too much head space will over oxidize your wine. If you can not figure out a decent wine to top up with then get some smaller carboys and bungs with extra airlocks. You will need these if you are planning on making fruit wines. If in a pinch, go to your local wine(liquor) store and get the argon or nitrogen gas in the spray can to preserve your wine. It is meant to do just this with a bottle of wine.