Lots of good info here. Lets start with a couple of things that look they have already been covered, but I want to make sure.
-- Download an owners manual if you do not have one. All of what you can and can not do is covered in the manual. Typically you are allowed two offsets. An offset is an elbow, a short piece of pipe and a return.
-- You have two different sections of pipe. Your interior pipe is either single wall or double wall pipe. In this case you will be much better off with double wall.
[I do not know what part of the country you are in but if there is an RW Specialties near you call them, ask for there sales rep. Alternatively go to nficertified.org and find a retail store with a certified salesperson. They should be willing to come out to your house, measure and tell you exactly what you need (I always did). They will also know what code and the AHJ will accept]
Keep in mind that typically a stove in the basement sits below the pressure point in a house. Add to that the fact that you have two offsets and you really might have some issues. The higher up those offsets are the better you will be.
You can do 15 degree or 30 degree offsets once you leave the house. there are very specific restrictions as to clearances to windows, corners, combustibles etc. Remember glass is considered combustibles as is any non combustible which is over a combustible.
Your pipe, on the outside of the house... Make sure you use ASHT pipe if available for your unit. Cold pipe cools down smoke and kills draft and causes creosote.
SERIOUSLY THOUGH this is not a forum question. Get a local person who knows the industry to check everything for you. It should be free. They want to make money on the pipe