I have been washing yeast for a long time, and always do so. Why throw away something usable, especially when its $5-8 ea. pack. I will answer your questons in order that they appear.
1) I have kept it up to a year, and still viable. But, I would recommend no more than 4 months. That is unless you want to freeze it. But that is a whole other monster. You cant just stick it in the freezer. There is a proper way, and a very detailed post on this site is available.
2)I store it in baby food jars, but mason jars work just as well. Just make sure there is no air (or the least possible) in the jar and keep closed tightly.
3) Once washed, you can use in any beer you want. Yo dont have to use it in the same brew.
4)ALWAYS SANATIZE EVERYTHING!!!!! The washed yeast is very easy to contaminate. I used to boil water to use for yeast washing, as seen in most processes on this site, or you tube. I found this kind of a waist of time. I now make up a new batch of star san and just use that instead of boiled water. I will sanitize my washing jars (usually 3 large mason jars) and pour all the trub into them. Then top off the jars with fresh star san mix,. Then pour back into the bucket, mix well, and proceed as you would normally to wash.
Now, a lot of people are gonna say dont do this. Star san this, star san that. Truth is, star san will not affect the yeast, or flavor of any future beer. I have been doing it this way for many years and have never had a problem. My yeast is always very healthy and viable.
5) and the last question. It all depends on the kind of yeast. Say, us-05, you will usually get enough to strait pitch into the next beer. But others can be harder to wash. Like belgian strong, I usually have to do a starter. The best way I have found is to split the wash into two jars, for 2 brews. Then just prepair a starter as you would for any other liquid yeast.
I have found over the years that yeast washing is a very easy and fun way to save even more money brewing beer. It becomes a whole other thing besides brewing. I now culture my own yeasts for friends. I even have a "house blend" of US-05 that is on its 26th generation. It tends to mutate itself for the procedures that you do. So now I have a yeast that no one else has, or can get. Unless you come to my house. Then with the right amount of begging, I may give you a jar
Others my dislike, and not approve of my method, but I have been doing it this way for a long time, and never have had any problems.
Have fun in your new venture and cheers