Decred has a hybrid Proof-of-Work/Proof-of-Stake model, which means that block rewards are shared between the miners and the stakers (and the developers), with PoW mining earning the larger portion of the reward. (60% PoW miners, 30% PoS voters, 10% Decred development subsidy)
The way staking works in Decred is through a ticket system. You purchase a ticket, and it enters the ticket pool. Out of the pool, a few tickets are randomly selected along with every block, and these tickets vote on that block. Every ticket has a 50% chance of being selected in 28 days, and a 99.5% chance of being selected to vote in 144 days, after which it expires, and returns to your wallet. For all the time that your ticket is in the pool, the DCR used to buy the ticket is effectively locked.
You don't need a full node to stake DCR. You can just be a part of a staking pool. A stake pool allows you to stake your coins along with the pool, which will have full nodes of their own running at all times.They will vote on your behalf, and take a small cut of your earnings (1-5% depending on the pool). Note that you do not give up access to your private keys at any point during this process.
Coming to your questions,
Yes. There is a minimum number of DCR you need. It is called the ticket price. Currently it is around 75 DCR (you can check the current price here), and it fluctuates with demand and supply of tickets. The age of the coins don't matter. But the ticket itself takes about a day to mature before entering the ticket pool.
In case you are using a staking pool, the question of upload/download speeds is now irrelevant. But overall, it is not a question of speed, rather availability/uptime. So if you're running a full node all the time, the staking part should be trivial.
At this point you can only buy full tickets. There are several requests for ticket splitting, which would allow you to buy a fraction of a ticket and stake regardless of how less DCR you own, but that really isn't priority on the dev pipeline. Also, there is a 0.5% chance that your ticket is not picked, in which case the amount you spent on the ticket will be returned to you minus any transaction fees.
For a good introduction to the whole system, the PoS Documentation is a great place to start.
The FAQs are a great resource as well.