Please keep the violin horizontal for the time being to minimize the risk that the sound post falls out of position (inside the instrument). If it does fall, you must not bring the strings up to their normal pitch until someone has re-positioned it -- you must leave them all a bit loose. (Unless the sound post has fallen, it's important to keep the strings to their normal tightness, and approximately in tune, to prevent the sound post from falling.)
I suggest you visit a music store Wednesday, Friday or Saturday and ask them to get the violin set up for you. The sooner the better because new strings lose their tuning quickly while they're stretching out.
Many music stores will only be closed on Thursday. They generally want to make as many sales as possible when people are off work.
The old-fashioned way of dealing with slippery or sticky pegs is to use chalk (like to write on a chalkboard) and soap. The new-fashioned way is to use a tiny bottle of a special liquid called Peg Dope. Peg Dope is a bit easier to work with but I really think that at this stage your best bet is to hand off this whole project to a music shop. I would call first because not all music shop employees are comfortable with string instruments.
It would be good to humidify the whole house and try to get the various rooms to have a similar humidity. You can buy a simple hygrometer for about $10, I think, at something like Lowes or Home Depot or an old-fashioned hardware store. You can humidify by running hot water through the shower into the stopped-up bath tub, and/or boiling water on the stove. (Work out your plan with your family before you embark on this, for family harmony.)
Later on you could buy a "dampit," which is a long sponge with a protective, porous covering. You would keep this moistened, inserted in an F-hole, with the case closed, during the dry months, but even when using a dampit it is good to keep the humidity in the house between 30 and 40%.
With dry air you might get some separation where some parts are glued together, because of glue drying out. If this happens we say the violin has an open spot, and you can get some rattling vibrations. It is often possible to repair this at home but it's a bit tricky if you've never done it before. I wouldn't want you to have to pay for a repair.
Re chalk and soap -- basically, chalk makes it slip less, and soap makes the peg stick less. It is possible to have a peg that both slips and sticks. They can really drive you nuts.
Sometimes a slipping peg can be dealt with by just pushing it firmly toward the center while tightening it. It takes experience, though, to know how firm is just right and how firm is too firm.
Do you have metal tuners on some (all) of your strings? If so, keep them pretty well extended in general, and don't try to use them until you've gotten the strings mostly in tune with peg adjustments.
The first thing I generally do with a beginner's instrument is loosen the tuners quite a bit, and then ask the beginner if s/he knows whether the pegs move easily, and whether they tend to slip or stick.
Everything in my answer goes for other string instruments as well.