I have the card Hadana's Climb and Riddleform in my deck, if I add the +1/+1 counter on Riddleform while it's on it's creature form from my Hadana's Climb will it stay there until the next turn that my Riddleform changes or will the +1/+1 counter disappear after then end of turn?
Yes, the counter will remain.
From the Comprehensive Rules:
121.1. A counter is a marker placed on an object or player that modifies its characteristics and/or interacts with a rule, ability, or effect. Counters are not objects and have no characteristics. Notably, a counter is not a token, and a token is not a counter. Counters with the same name or description are interchangeable.
You can put a counter on any object on the battlefield, as long as that object is a valid target when the ability/spell that puts a counter on it resolves. You can only put a +1/+1 counter on Riddleform using Hadana's Climb's ability if Riddleform is a creature, but any +1/+1 counters already on it when it stops being a creature will remain. It's worth noting that, since +1/+1 counters only have an effect on creatures, they'll essentially do nothing while Riddleform is an enchantment.
Yes, your Riddleform will keep the +1/+1 counters on it.
Permanents don't generally care what counters are on them unless they have and effect that says they should care. So even when your Riddleform turns back into an an enchantment it will still have it's +1/+1 counters on it (even though those counters won't do anything).
One special case to note is that your Hadana's Climb can only place +1/+1 counters on creatures. So even if your Riddleform has already received a counter or two, you will not be able to place additional counters on it with Hadana's Climb (and then cause the transform) if it is not currently a creature.