D&D 5E Ranger- Soldier Backround with panther

1: Can or can't the ranger have a bonus action ATK with duel wielding from offhand weapon? I've read some older posts and this is my first time playing. Our DM is well versed but I want to have the correct information on my creature sheet.
I know the panther has keen smell and the ATK's Bite and Pounce, Pounce providing an additional ATK as bonus action> (if the panther moves at least 20 feet forward and hits with claw ATK and the target fails on a DC 12 Strength saving throw or is knocked prone. If target is prone, the panther can make one Bite ATK against it as a bonus action.)
However, i don't understand the Dual Wielding bonus action which is my question mentioned first.
2: I do not understand why the 2 ATK's the panther has are both listed as Melee weapon ATK +4 to hit but the damage is 4 1d4 + 2 slashing for pounce and 5 1d6 +2 for Bite. I'm not referring to the die, rather when to apply the melee +4. I'm currently trying to fill out the creature sheet and have no idea where to write it. Thanks for any help and patience, as i am a newbie!
-JLD

1: Anyone, including both the ranger and wizard, can use their bonus action to make an off-hand attack if they used their action to make an attack with their main hand.
Note that you do not get +Str/Dex to damage when you Two-Weapon-Fight, unless you have a feature.

2: The attack roll is 1d20+Str (or Dex for finesse weapons)+ your proficiency bonus.
The panther probably has 14 Str (+2) and +2 for their proficiency bonus. = +4.

Damage is your weapon (1d4 for claws, apparently) + your str/dex (+2).

thank you so much mellord! I've been trying to wrap my head around this for nearly two hours now!

You need to look at which rules you use for an animal companion. Are you using the Unearthed Arcana article for the Revised Ranger?

Generally speaking, any character that has used their action to make an attack with a light melee weapon can make another attack as a bonus action on that turn with a light weapon in their other hand, but it doesn't add the ability score bonus to damage. However, this uses up the bonus action. Accordingly, if you use the bonus action for another purpose, such as casting (or moving) Hunter's Mark, then you can't do it.

If you're using the revised ranger rules, the panther would have their own set of actions, and thus what it does would generally have no impact on your use of bonus actions.