had to quit app and rerun it and after using ctrl-c i lack one record :
More likely it seems to me, you have one unassigned block_id. This is not the same as a missing block. block_id is an internal identifier, not visible in any HTML or API output. So it doesn't really matter what the block_id is. It will vary from one Abe instance to another for the same block. Abe allocated a block_id but hadn't used it when you stopped it, so it remains unused. This is not a problem.
By the way, the visible "block number" is called "height" internally. Often height and block_id are numerically close, depending on how you load the data, but they will diverge if, for example, your block file contains side chains or you load Testnet or alt chain data along with the main BTC block chain.
Is here any possibility to recheck for missing data?
It would be nice to have a validation tool that checks for missing data. We don't have that. Part of it is covered by the foreign key constraints, and there is a tool (Abe/verify.py) that verifies the transaction Merkle hashes, but it could do much more.
If you haven't done anything like delete table rows, and barring any bugs, if Abe shows a block number, it has all data from the genesis through that block.
Another thing - when i have bitcoin running - can i rerun app to check for new blocks, or i have to stop bitcoin?
I have never noticed a problem running both at once.
And btw - how is this tool different from Bitcointools ? i am new to this tools, was using crappy json-rpc methods given in bitcoind : p
Abe borrows some low-level code from Bitcointools and adds many features, notably SQL database support, speed improvements through indexing, and the HTML interface similar to Bitcoin Block Explorer.