Matt Murph, good luck, there is no real answer and it all depends on your goals, what you will do in the worst case, and your risk tolerance.
To address the easy stuff first: Why are you only earning 0.2%? You should be able to earn at least 0.8% percent in an FDIC online savings account with no work, and maybe 1-3% on at least some of that money relatively safely if you are willing to jump through some hoops (rewards checking, short term CDs, credit union promos, etc). I'd do the first for sure, you can decide if the second is worth the trouble. The difference is only a few hundred to maybe a thousand a year, but every bit helps :)
To answer the second question, we were in a similar boat a few years ago and a good post on Bogleheads (which I unfortunately can't find right now) helped informed my thinking on the subject. I think our approach worked out well for us. It came down to thinking about how certain are you that you will buy the thing you are saving for, how certain are you about the timeframe that you will need to make the purchase, and what are the consequences and fall-back options if you don't have the required amount at the required time.
If for example, your doctor told you that you would absolutely need a new pacemaker in 2 years, you knew exactly how much it would cost, and that you were SOL if you didn't have the money in two years, then you know for sure you better save exactly that amount and have it ready in two years, you don't want to take market risk and you put in the safest vehicle possible.
On the other hand, you might be in a scenario where you possibly maybe want a house down-payment 1-5 years from now, or whenever the time is right, you don't know how much you want but know that more would be better, and that your comfortable with the back up plan that if something goes wrong you can either put off buying a house, or just make a smaller down payment, then you have a different scenario than the first example.
With that in mind, we decided we would all our money according to our desired asset allocation (60/40 in this case, we are conservative), across all accounts, taxable and tax deferred. In the the 40% fixed income category, we included all cash, savings accounts, CDs bond funds etc. Ultimately money doesn't care whether it is your "emergency fund", "new car fund", "down-payment" savings, etc. Your overall return is going to be driven by the combination of all your accounts, so why not treat it as one asset allocation.
When we did end up buying a house (somewhat quickly and unexpectedly), we just tapped the cash in our high-interest savings accounts, CD's etc, sold enough equities in our taxable account to make up downpayment we wanted, and re-balanced across all our accounts back to the desired allocation once the downpayment was withdrawn.
This worked great for us, partially because of timing and market returns over the last few years. But those are things you can't control or predict. If shit had hit the fan, we would have either just continued renting, made a smaller downpayment, liquidate a larger percentage of our equities, or packed up and lived in a van somewhere.. no big deal either way :)
That's just my two cents and experience. Hope it was helpful.
I couldn't find the original bogleheads thread I had read, but this describes something similar to what we did:
http://www.bogleheads.org/forum/viewtopic.php?f=1&t=131025#p1929021