"Relayed By"

Bitcoin Core doesn't track which node relayed a transaction, and I doubt most other nodes do either. In addition, this information is likely to be different for different nodes as each one may first receive a transaction from a different peer.

figure out hash rate of specific mining pool as a % of total in the real time

Full nodes don't have the information necessary to determine anything about mining in real time as they only receive information about blocks when those blocks are distributed (on average every 10 minutes, but with high variance). Because block finding is so variable, it's additionally necessary to average results over large numbers of blocks to get reasonably accurate numbers, meaning the statistics you typically see are either trailing actual block production by several days or are probably quite inaccurate.

In addition, miners don't have to identify themselves in the blocks they create, and the way they do optionally identify themselves is not standardized, so no stock full node provides any method for telling you which miner created which block.

Block explorer websites will run full node(s) of their own, and then use data obtained by their node(s) to calculate and present much of the info shown on their website. Not all info shown on the block explorer sites is explicitly present in the block data, some may be calculated or inferred by the block explorer website.

Relayed By", there was a block that was listed as unknown on blockchain.info and showed as "relayed by" by specific mining pool on btc.com

This information is not present in the block, so block explorer websites must use another method to determine it. Note that the peer you hear about a new block from is not necessarily the peer that mined that block.

Is there a way to figure out hash rate of specific mining pool as a % of total in the real time.

This information is also not included in a block.

The total amount of hashing power pointed at the network cannot be measured directly, rather it can be calculated by considering the current difficulty, and the rate of block generation. Knowing the total, you can count how many blocks (of the last x blocks) were generated by a certain pool, to estimate that pool's share of the total hashing power over that time frame.

Note that there is no requirement for a miner to put their name on a mined block, but historically many miners have elected to do so.

For these reasons, it is not possible to make a real time measurement of the hashpower controlled by a certain pool, and even the method described above is not guaranteed to be accurate.