I'm new to bitcoin and have a couple of probably dumb questions.
1. my wallet address - does it ever change or can I use the same address forever?
You
can use the same bitcoin address forever if you want to, but you don't have to.
It can be better and safer to use a new address for every transaction. There is no limit on how many addresses you can create if you want. An address is NOT an account number. It is just a way for your wallet to identify a transaction that has been sent to you. Using a new address for every transaction gives you a way to track and account for all your transactions. It also increases your anonymity and security a bit.
If you decide in the future to switch to a new wallet software, it can be a hassle to try to export an address from one wallet and import it into another wallet. If you use a new address for every transaction, then there is no need to import any addresses to a new wallet.
2. Yesterday I recieved three .0000001 transfers to my wallet (on my computer) all with the same time stamp. I have signed up anywhere for free coins.
Somebody generated a list of every bitcoin address that ever received any bitcoins from anywhere. Then they started sending extremely tiny amounts to each and every address in their list. They paid an insufficient transaction fee for the HUGE number of bytes it takes to send a single transaction to that many addresses, so the transactions will never confirm and will eventually (within a few days) simply disappear. This is a spam advertising technique, and a rather ineffective one. You can just ignore these transactions. They won't have any effect on your wallet.
I read somewhere that when you move BITCOINS from your wallet there is sometimes "dust?"
If you receive LOTS of extremely small value transactions that all sucessfully CONFIRM and are therefore usable by your wallet, then they can increase the transaction fees that you will have to pay when you try to spend that value later.
or is this someone trying to gain access to my wallet?
No. This will not allow anyone to access your wallet.