1) The brokerage will typically not calculate the cost basis for shares that are not purchased through the brokerage. In this case, you transferred the shares in from your 401k.
a) At the time of the transfer you paid the tax. At this time you therefore calculated the value of the shares. If you transferred 100 shares and paid tax on $1000, your cost basis per share is $1000/100 shares=$10.
2) No, you only have long term if you have been the beneficial owner of the shares for over a year, as in 365 days. This is a factor in when you choose to sell the shares.
3) You will need to enter the date you initially received the shares, the cost basis you calculate, and report it as a sale where cost basis was not reported to you by the broker. (There are 4 categories, short term covered (e.g. reported basis), up to long term not covered (basis not reported.) TT has a drop down for this when you're reporting the sales. You report each of the 4 types of sales separately. It sounds like you are probably going to report as D: long term not covered.
