SMD diode value

Very good idea to practice, practice, and practice some more on salvaged boards until you get competent with new tools. You didn't notice the solder had reached the molten state because there's so little of it used to solder components.

The typical lead-free solder has a melting point around 217 degrees C, so you'll have to get the leads and pads up to that temperature before trying to remove the component. The reason why you need a much higher temperature is because you want to get the solder joints to the melting point as fast as possible. If the hot-air gun is set to a much lower temperature, it'll take a longer time to reach the melting point. The longer the time to raise the temperature of the leads/pads will increase the overall temperature of the component, possibly past the point of destruction. So the technique is to heat it up fast, remove the part and hot-air gun, then put the part where it can cool off.

Now, if you're removing a part that's already fried due to some other reason, no worries then. Just don't damage the board by overheating the pads and causing them to lift off. If that happens, your headaches are just beginning on this repair.

No need for solder paste.

I use an RMA rosin flux pen (it works like a Sharpie) to coat the pads (especially the big one) with flux and then solder. Liquid flux with a brush works well too. Heat the big pad and tab from the side and introduce enough solder to get it thoroughly attached. If the board is reasonably fresh it will suck the solder in under the large pad quite readily. Liquid flux and flux pens are a bit of a pain because they can't be shipped by air, so they're easiest to buy locally. Liquid flux in large quantities even attracts a Hazmat shipping surcharge.

Make sure the part is quite flat before soldering with essentially no gap before introducing the solder.

If the part does not need to dissipate much power (for example, a regulator where you don't expect more than a few hundred mW) you can just tack the end of the tab rather than flowing the solder right under. Make sure the connection is solid- especially on the DPAK package (the one you show is a D2PAK) because a lost ground on a 3-terminal regulator can have unfortunate consequences.

If, for some reason, you have to remove the part and replace it, clean the pads thoroughly by sucking up the solder (for example, with fresh solder wick) and make sure the new part sits dead flat on the cleaned board before attempting to solder it on.