Do you need to download the entire blockchain in order to mine bitcoins? I'm downloading bitcoin-qt, and I'm afraid it will take up too much memory on my computer. Also, I just read that when another node downloads the blockchain from me, that will also tie speeds. Is this true?
If you are solo mining, then you need the entire blockchain since each block you mine references the hash code of the last block in the chain. If you don't have the last block yet, then the network will reject your mined blocks since there will already be later blocks in the blockchain.
If you are mining in a pool, then you don't need the blockchain or bitcoin-qt. Just point your miner at the pool and start mining.
If you mine in a pool, the pool will send you whatever work you are mining on, i.e. you don't need to download the blockchain.
If you are solo-mining you will need the blockchain.