Increasing the odds when solo mining with low-medium hashrates I never saw anything concrete related to this so I dare to ask here.
First, my situation: 
I'm currently mining solo, on a private pool, with roughly 350Th/s. That to be increased soon with another ~200Th/s. 
I know my odds, right now, from the plenty online calculators, I should solve a block roughly once a month at this diff. 

But, would either or both of these following measures increase my chances? 
 - First is running the pool bitcoin daemon as a full node with port 8333 open to the world. 
 - The second is lowering the relayfee which is default to 0.00001000B.
No, neither of these things will help.

The only thing that really affects your chances is your hash rate, and the measures you describe do nothing to help it.

One other thing that can make a very slight difference (&lt; 1%) is latency: the time it takes you to receive new blocks from the Internet (or work from your pool), and to send out your own.  In the unlikely event that you find a block very close to the same time as someone else, these would slightly increase the chance that your block is received first by other miners, and thus decrease the chance that it is orphaned.  But if your pool servers are properly run, they should be doing this pretty efficiently already.  Maybe faster than your own full node would be.

The relayfee has no relevance to mining.  If anything, you'd want to increase it, so that you relay fewer transactions and thus save bandwidth for receiving and sending mining work.  But this effect would likely be negligible anyway.