I'll try my best, but I'm still gaining info about the libertarian party.
*The Post Office - this one's easy...
Less junk mail.

Seriously, since I can pay practically any bill online and even get magazines through e-mail, there's really not much of a reason for the postal office to exist. However, if a service was still in demand, we would have competing businesses for the delivery for mail, just like we have FedEx and UPS for package delivery.
*Unemployment Compensation - What would happen when we lose our jobs and didn't have the money to pay bills?
In a libertarian world, this issue wouldn't be much of a concern because the much less government regulated free market would allow you to find a job quicker. Instead, we get these stupid special interest acts such as NAFTA which kills our jobs. But that's for another thread.
Anyway, a libertarian president would enact a consumption tax and get rid of the income tax. So how does this affect you when your unemployed? Well, you would naturally want to consume a lot less, so you would pay less in taxes. In addition, there are alternative options for income such as CDs, bonds, and even the stock market if you know how to play it well. If you can manage your money and show that you're a good worker, then I don't see the lack of unemployment insurance as a problem. The real issue here is that most Americans expect all of these handouts from the government and don't take any responsibility for what they spend, so as a result they get into these big debt holes where they're stuck in it.
*Abortion fully legal?
Mmm, depends on who you ask. I believe that an unborn child still has rights and abortion should only be used in special situations such as if it could harm the mother, the mother is still a child or young teen, the child is going to die, or if the child will live a very low quality of life. Even then, one can still put the child up for adoption.
On the other hand, it's not like every mother is going to get an abortion just because they don't want the child. In this case, I can see the libertarian viewpoint of just staying out of the messy picture period and not giving preference to one side or the other.
*Legal drug use
A lot of people think that if we somehow make illegal drugs legal, then everyone is immediately going to run to the pharmacy, get high and this country will immediately fall apart. In reality, the drug laws have made the situation much worse because of the crimes that have followed the illegal trade. Take for example, the probation acts of the 1920s. When alcohol became illegal, what happened? Speakeasys popped up & the trade of alcohol was controlled by organized crime. If we legalize drugs, not only will the illegal trade begin to dissipate but the crime that comes with it will also eventually shrink down to almost nothing. That, ladies and gentlemen is how you win the War on Drugs.

*Medicare / Medicaid
Simply another government tool that doesn't work. Get rid of it.
*Social Security
Heh, I find it funny that despite the fact that my income is being deducted for Social Security, there's no guarantee that it'll be in my future. The system is managed so badly that it just needs to be cut out. Plus, the paltry income that comes with SS when you're 65 won't be enough to sustain you anyway. You still have to manage your money anyway, so cutting SS out will give you more money to be able to save up for retirement.
*No government involvement in healthcare
Same thing with Medicare/Medicaid, only this problem will be about 100x more massive. For some reason, Democrats think that by copying the models off of Canada and other European countries, we'll suddenly have happy joy and paradise. What they don't realize is that our population is a lot larger than most European countries and a lot of the medical infrastructure would have to be shut down to fund it, which would also create unemployment. In addition, your taxes will have to take a huge hike to fund it. Not a very good solution. Instead, we should keep it private, but encourage more businesses to offer healthcare coverage and get them to compete with each other. Competition is what will keep prices down.
*Environmental concerns
As stated above, the government is the biggest polluter because it allows corporations to pollute. To use another example, if I stabbed or did some sort of harm to you, wouldn't you want to press charges against me? Wouldn't you want me to pay for the damages associated to your health? If these companies want to pollute, then they should pay for the costs of those affected by the pollution. That's also another method for pushing renewable, clean energy sources.
*Weapons
As stated in the Second Amendment, you have the right to own a weapon. If you use it responsibly, then there's no harm done. If you attack or kill someone for your own benefit, then you've not only broken the law, but you've violated someone else's civil liberties an you should be punished for doing so. Just as with drugs, if we put all these bans on weapons, then that will only fuel the illegal trade.
I hope I was able to answer some of your questions.