Separation anxiety is completely normal and expected for a 19mo. Every child is different, so every child has it to a different degree (my son was clingy, my daughter adventurous), and every child outgrows it at a different age (my son was just over 2, and my daughter went in and out of spurts until around 20mo). The best suggestion I have is to spend some time in the gym child care with him, play with toys, and get him familiar with the environment before leaving him in there. This could take a few days to a couple weeks, but it could be well worth the effort in the end :)
As for the sleep "issues," your 7mo isn't the one with the sleep issue. It's society's unrealistic expectations of when a child should STTN or how many times they're "supposed" to wake during the night at any given age that set us up for unexpected and frustrating variations to what it unrealistically set as the norm. It's perfectly developmentally normal for your 7mo to be waking 2-3 times each night, and honestly, sleep training is pointless during this huge developmental leap. Even if the "training" works, sleep patterns and habits change so frequently that you'll feel like all you're doing is "training" your little one to sleep. The period from 4mo until just over a year is a period of HUGE change! Rolling over to sitting up to pulling to stand to crawling to cruising to walking.... It all happens so fast and can be a little scary to someone so little.
It's also perfectly developmentally normal for a 7mo to need a little reassurance and assistance to fall back to sleep. Try to think about the myriad of reasons he could be waking: hot/cold, bad dream, lonely, scared, wet diaper, hungry, upset belly (from solids possibly), just needs to be close to mom, etc etc. Also, try to consider why we wake as adults and give the same consideration. I personally had a very vivid not-so-good dream a couple of weeks ago that stuck with me from the time it woke me at 2:45 until my alarm went off at 7:15. If that can happen to me, it can certainly happen to a baby who has no experience.
It's very possible that he's hungry each times he wakens. However, you're probably correct in assuming he's not hungry every 2 hours during the night :) If he does ok with the water, maybe snuggle him with his water bottle for a few minutes, then slowly move away from him. With separation anxiety beginning around this age, I don't think it would be a good idea to move him further from you, especially since you'll then have to get out of bed, walk to a different room to settle him, and walk back to your bed.
Teething could definitely be a culprit; you could try using a small dose of infant ibuprofen (fever reducer as well as swelling) the first time he wakes.
His sleep will change many times over the next few years, and he may not STTN for a long time yet. My son didn't sleep more than 2-3 hours at a time until he was almost 2, and I thought I would die from sleep deprivation. After age 3, he slept better, but both my kids (almost 7 and almost 4) still wake in the middle of the night to crawl into bed with us. (my husband and I sleep in separate beds for a variety of reasons hehe) Remember that a lot of nighttime parenting has to do with our own expectations, experiences and attitudes :)