In lieu of hot air, I recommend using "ChipQuik" for the SMD capacitors. It significantly lowers the solder's melting point, and (in my experience) mitigates the risk of damage to pads already weakened by leaked electrolyte.
For repairing the pad, it can be done perfectly (so don't fret too much!), or as mentioned, a small bit of wire soldered to an adjacent via, or scrape away a bit of solder mask from the trace leading to the pad, and attach a small piece of wire there (about the length of the original pad), then solder the cap in place. (Kapton tape can be helpful, but it will be fiddly regardless.) These later methods can be reliable, but it's worth taking the time to learn to do "perfect" if at all possible (copper foil and adhesive).
In addition to what's been mentioned, a stainless sewing needle might help with the broken through-hole pieces. You can use a bit of ChipQuik on those too, carefully rock the part a bit at a time until it's free. However, a quality desoldering gun is probably the way to go here. Stay away from the cheap plastic "soldapult" type devices, the recoil causes the tip to nick the PCB, causing damage.
