No, don't use a hotplate to reflow.
If you must use a hotplate for preheating, that's fine, of course a purpose-made one is preferable.
Hot air can be used the same way, perhaps with some insulation around (Nomex or fiberglass pads?) to reduce heat loss. I've had to do that before, put insulation around a large object to make a sort of oven to get the thing up to temperature; but that was also a solid copper assembly, an exceptional case.
I've done DFNs on boards with 8 layers of planes, just takes a long time before the whole board gets warm enough the hot air can do its job. In that case, I merely tin the pads, apply flux, and place the component. In time, it settles down, and I can give it a nudge with tweezers to ensure it's seated, has the correct amount and distribution of solder, and likely doesn't have shorts under it. If it has too much solder, I can push down and squeeze out the excess, wick it away and try again, perhaps with another dose of flux. For DPAKs and such, where a toe or side fillet is visible, this last step is not necessary, you can see immediately how much solder is in the joint.
You clearly have little or no experience using hot air. Get a machine and practice using it. Set the temperature a bit above soldering temp, set the air flow as needed (for a board like this, you'll probably want max flow and a large nozzle), and wait. If it's not melted in say 5 minutes, turn up the heat and wait some more.
The last thing you want to do is burn the shit out of it, with an uncontrolled heat gun, or a hot air machine set way too high. That's why it's temp controlled, so you can't burn it up, at least not very quickly.
Chip components will not be blown away, at least not with a common machine. If it's blowing that strong, turn it down, duh. They also will not fall off the bottom, if the bottom side should get hot enough to melt. Surface tension is quite strong compared to the size and mass of these components.
Tape is not advisable, as it will tend to lift and pull components if they happen to melt.
Tape and foil can be used as heat shields, say to keep hot air away from connectors, electrolytic capacitors, etc. Use polyimide, preferably with silicone adhesive. This may not be helpful if the board has internal planes, i.e. you need the heat applied to most of the board, not just a local area.
Ed: also, regarding reflow, it's not so much that it may be expensive, as it's just awkward. To put it on the production reflow oven, it needs to be fixtured, and the fixture may need PCB rails that have been stripped off at this stage of assembly. So you'd have to cook up a replacement first. Reflow also doesn't help with removing the component, or cleaning the pads. Hot air and soldering iron is the correct rework method here.
Tim