The number of shares purchased, how much KRAM coin purse kept inside?
More than 30 days?
Would like to continue buy shares of the wallet address confusion afraid generate another address

I hope that a future version (in the not-too-distant future) can let the share explorer know of all your wallet addresses so you can just automatically log in to it.
But you can look at your transaction ID on the left side of the page now. If you want to test the address you see for it you can send yourself 1 karma. You should get it immediately. (We'll make it searchable and sortable eventually.. We can do it now but updates would be only every few days instead of 3-5x a day.)
Yes, you can keep them for more than 30 days. If you want a full quarter of profits you should keep them at least 3 months. (30 days would only get 1/3 of the profits for that quarter. Profits for the quarter would be announced after the quarter is finished.)
Hope this answers your question. Let me know if you have any others.