1) Should I significantly increased my 401(K) contribution? I'm not sure I have ability to max it out yet but I am currently only putting around $4k/year in so there is room for improvement
You should first make an Investment Policy Statement which states what you should do. So it may read:
I will first max my 401k to the match, then my HSA, then my Roth IRA, then my 401k with extra up to the maximum yearly limit, at which point I'll invest in a taxable account for retirement.
2) Going along with above, I want to make sure I leave myself ability to be able to buy a house (not earlier than 2-3 years from now though) but considering how much liquid $$ i have now (relative to my total) should this not prevent me from aggressively increasing 401k contribution?
If you want to buy a house you will need to allocate a portion of your non-retirement savings to that goal. Perhaps create a new taxable account specifically for that purpose and build the savings there. But yes, if you're getting the match on your 401k and maxing your Roth and still saving more then I'd save for the house.
3) Instead of putting more of my current dollars into taxable accounts should I explore something like Lending Club for some diversification?
I would do your diligent research before I dumped money into P2P lending.
4) Should maxing Roth out continue to be a focus going forward (it has been for me since funds can be used for purchase of first home)
With your yearly savings amounts you should be maxing your Roth every year.
5) How do I determine when/how much to put into my taxable accounts, currently I just put in $5K or so whenever I feel like it, I haven't done so since March because I have been apprehensive about market and I know this is not a good reason to hold off
Again, you should make an IPS which will state how much you should put into each account and when. You may consider dollar-cost averaging a bit in each month automatically in order to take the guess work out of it.