I would definitely agree that a toddler of 16mths should be having a daytime nap, but perhaps you would have more luck if you tried one nap towards the end of the morning/early PM.
If your DS is up with the larks, then perhaps a late morning nap BEFORE lunch might be best. If so, and you find he is getting grumpy by late PM, bear with it and try and get him down half an hour earlier than usual (6-6.30pm), as they often don't sleep so well if they are overtired.
I'm sure we've all had the same problems with our DC dropping naps in the day, but I think most kids of 2-3 are still having a short nap. If you have someone else at home during the day who could help you (DH, MiL etc.) then see how your DS reacts to being put down by them. I think at 16mths he might be "trying it on" a bit with you. My own DS dropped his naps for a week at about 20mths, but was clearly shattered. In the end I had to just let him cry it out - the first time I had used this method - and I felt horrible, but within 2 days he was napping again.
The getting up early is also really common, and there are lots of threads currently running on this one. You could try:
(1) blackout blinds
(2) the "kidsleep" clock (although recommended for older toddlers, it has worked with our own from about 22mths)- you'll find them on the net
(3) going in at regular intervals (10mns) and saying "It is nighttime, time to sleep" - but not making eye-contact or giving him any other stimulation. It might take a few days, it might take a week, but eventually he'll get the message.
Personally I think it is really important you encourage your DS to stay in bed until a time when you feel YOU are able to cope with rising - we had nearly 6mths of "early waking" last year and it nearly killed us. With number 2 I think we will probably just be a little firmer with him; at the end of the day you do your very best, but you need your sleep too and unless you are able & prepared to go to bed at 7pm yourself, you cannot be an effective and cheerful parent if you are not getting your full quota.
That said, the best piece of advice my mum gave me was to go to bed at the same time as the kids (or near enough) at least once a week. It's the new parent equivalent of the Saturday morning "lie in".
All the best.