Yes, DPSK lets you assign dynamic VLANs.
And yes, the tunnel passes DHCP traffic. So if DHCP is correctly functioning for a VLAN at your headquarters then it should function correctly for the same VLAN at the remote end of the tunnel.
DHCP relay is an L3 thing. The tunnel is L2, so you just want to make sure it's not blocking DHCP. You can
see here, that even blocking broadcast traffic doesn't block DHCP.
Yes, placing at the same site is fine. Ideally place it on the same subnet, and assign a management interface.
SmartZone is free to download and trial, for up to 5 APs, for 90 days. And they have videos on youtube to walk you through the initial setup.
If you need a longer 'trial' then just backup your config, reinstall vSZ, then restore your config backup. Ad infinitum if you can be bothered.
Ruckus One is free to trial for up to 100 APs, for 180 days. And they'll generally give you a second trial if you run out of time.
An advantage of these controllers is that you get very fine-grained control over where DHCP happens, and which traffic goes over the tunnel vs local breakout (so e.g. your APs could directly hand out DHCP addresses, tunnel internal-app traffic back to headquarters, but dump printer and internet traffic out to the branch network).