It would not take 4 billion years at the speed of light, it would take 111 years. That's what light-years are, the distance travelled by light in a year.
Strictly speaking, if you actually traveled at the speed of light, the trip would be instantaneous from the reference frame of the craft making the trip. It would still take 111 years from our frame of reference on Earth.
Also assuming no acceleration or deceleration time in this made up impossible scenario. In the more likely scenario where we can get to a fraction of the speed of light using current technology we do have to account for both factors in both time and space probe weight.
Yes, but we can't actually travel there with our current technology, and while you're speculating about future technology, you can pick the number of 9's to tack on to your cruise speed pretty much arbitrarily. So from the probe's perspective, it takes somewhere between a fraction of a second and many billions of years to arrive.
Nitpicking: Virus are a bad choice. Most are highly specific and reuse a lot of the machinery of the cell they attack. It's much better to send a mix of bacteria and archaea (ask an specialist to get a good combination of strands that like to live in different conditions (hot/cold, oxygen/no-oxygen, ...)). Put them inside a shell to protect them from radiation and a good shell for landing/crashing (ask another specialist for this part too), perhaps like a multiheaded interplanetary missile with many a copy of your minizoo.
Probably anything you send has enough bacterias to have a chance, unless it's super clean an sterilized. They try not to send bacterias to Mars, but I think bacterias will win. They only need a single error to get a free trip.
I remember a joke that someone said that Eukaryotes is the method that Prokaryotes use to travel from planet to planet.
If the goal is to seed life, why not send something already alive instead? Though I don't think we know what to send that would be a living colony still by the time it arrived, even if we knew how to send it exactly. And it'd probably just die when it arrived unless we get a much better idea of what's there already.
An artificial intelligence would likely be the best bet actually, but there's a bunch of challenges there we don't actually know how to solve either. Maybe in a few decades there will be fewer unknowns at least.
There are people working on the basic technology [0]. It's going to be quite a while before we visit nearby stars though. Even launching a probe that has a reasonable chance of successfully visiting (and communicating back to us!) this star system is probably not going to happen in the lifetime of anyone currently living.
