It is common for a newly planted lemon tree to drop its fruit; it will take a few years for its root-system to be developed.
every 3 days for the first month
Should a newly planted tree have the lower branches cut to encourage faster growth?
Yes .
For the first year make sure they have sufficient water and the plants cannot rock in the wind.
Move it.
Stake it to avoid rootball movement and keep it well watered during the first year.
Yes they will eat the lower new leaves and ones higher up too if they can get at them. They will also have a chew at the bark and if left to their own devices will ruin a newly planted hedge. Hares will decimate a newly planted hedge. They chop off the stems and strip the bark. If either beasts are attracted to a newly planted hedge fence it with chicken wire--both sides.
4th
it's because you are watering it to much
Any organic material will do just make sure the ground is well watered before you put the mulch on.
depends on how much damage it took