Regarding #1, I'm feeling the larger market is overinflated and while I know timing the market is not typically the way to go, I'm hesitant to dump a lot of cash into anything in particular. We are already maxing out our 2 401k's and IRAs annually.
The one thing it seems you definitely do value, and would consider 'dumping a lot of cash' into, is paying off the house. It's a valid emotional win to do this, and considering it's akin to getting 3.25%+ return, in that you won't pay future interest on that mortgage, a positive gain for your net worth.
My house has gained about 8% a year in supposed value, averaged out over approx 10 years. Personally i'd be happy with an 8% average return on my 401k investments over time. So for me, i would look at the issue like i was paying off a 3.75% mortgage, plus my investment [ the house] was going up in value. I count my home equity {minus a reasonable amount of sales transaction costs} as part of my net worth.
Now of course this # assumes i have no maintenance costs on the house. Real estate Taxes i'd leave out of the equation as they are owed to the state/county for local services, their cost is independent of how much i owe on the home, and a renter is still essentially paying towards the landlords real estate tax obligation.
Why not pay off the $80K and end the mortgage? Have a small mortgage burning party like previous generations did. Then use the balance $100K toward after-tax investments. You can then take the money you would have been putting toward the mortgage principal, and dollar cost average it back into the market monthly over the next several years. You get an emotional win, you get a financial win, you'll only have to find a place for ~56% of the total starting amount.