How come I have been paying my mortgage for 2 years, but the balance is actually growing?

This very unpleasant situation is called negative amortization. The most likely causes are:
i) You have an adjustable rate mortgage with a payment cap that does not allow you to raise your monthly payment enough to match the new interest rate. As a result, your monthly payment is probably high enough to cover the principal part and some of the interest, but all the underpaid interest is added to the outstanding balance. The situation calls for emergency action!!!
ii) You have an option adjustable rate mortgage and you stick to the minimum payment option, even though the rate has changed. If you have ignored the raised rate for 2 years you are in big trouble, because most option ARMs carry a 7.5% a year minimum payment cap. Under such a limitation it is very problematic to catch up with the new rate and the debt it has already produced. The only way out of this is selecting some other option for your monthly payments immediately; otherwise negative amortization can increase your debt to a virtually unpayable amount.

How come I have been paying my mortgage for 2 years, but the balance is (practically) unchanged?

The reasons for that can be:
i) If your have a conventional fixed-rate or adjustable rate mortgage, and it is really as young as 2 years, it is natural for the balance to reduce insignificantly because of the “leveling” of monthly payments. You can find a more detailed explanation in my article about FRMs; but in short, in early years each monthly payment pays mostly towards the interest. Only in later years the monthly proportion of money paid towards the principal increases and then the reduction of the outstanding balance becomes more noticeable. The principal payment is always a remainder - the total monthly payment minus the interest; and if with a FRM everything is pre-calculated and the monthly amount is set, ARM monthly payments change to meet the new rate and serve, first of all, the interest; the principal gets the residual. Generally, this case presents nothing to worry about.
ii) If the balance is totally unchanged, you probably have an interest-only mortgage, i.e. everything you pay every month is paid towards the interest only.The balance will start to reduce only if you make an extra payment or when the interest-only period is over. For more details on Interest-Only mortgages read here.

How to avoid PMI or get rid of it sooner?

A borrower has to pay Private Mortgage Insurance (PMI) only if he cannot make a 20% down payment. So, the ways to avoid the insurance are the ways to find enough cash to be able to pay at least 20% of the price of the property in question. Nowadays, the following options are available: a second mortgage; a “piggyback” mortgage; and lender-paid mortgage insurance.

If you already have a mortgage with PMI, you have to bear in mind that you have all the right to have PMI terminated as soon as the outstanding balance hits the 80% of the purchase (or recently appreciated) price of your property. “Recently appreciated” is your opportune key to freedom. If your property has appreciated in value, the absolute amount of 80% of its current price is higher. What’s your advantage? Say, you have a property that was $100.000 worth when you bought it. 80% of this amount is $80.000. This is the magic number that allows you to cancel PMI. You have been paying the mortgage off for some time and your current outstanding balance is $90.000. If your home has appreciated, say, $10.000 through these same years, its current value is $110.000. 80% of this amount is $88.000, which means that with your outstanding balance of $90.000 you are only $2.000 (not $10.000) away from canceling PMI. Neat, isn’t it? Terminating the insurance, however, is not an easy business. Read about the troubles and tribulations involved in my special article. Yet, just one more thing that I want to draw your attention to – the appreciated value of the house has to be documented by an appraiser, accepted by your lender. The procedure is not cheap, so you have to see first if the appraisal will really save you anything in the long run.

Another way to shorten your PMI period is good old extra payments towards the principal. If your mortgage carries no prepayment penalties (any more) each extra penny towards the principal will bring you closer to the 80% margin.