1) Cum adulesceme iam satis roboris habebat cottidic corporis vires exercebat.
Is adulesceme ablative of adulescent, entis?
If it is, my translation would be:
With youth already enough strength had and daily exercised powers of body.
2) Theseus facillime lapidem movit, patris signa cepit et periculosa via ad patrem iter audacter fecit.
Theseus moved stone easily, took fathers signs and bravely headed on dangerous road to father.
The original document was OCRd and these are the mistakes:
Fons digitaliter transcripsi et vitia sunt ità :
adulesceme = adulescente (adulescens, entis in the ablative as you suppose, adulescens vel adolescens ablativo casu, ut suspicaris)
cottidic = cottidie
Salve Boban
Quod verto:
When he was a youth, he had more than enough strength and exercised his body’s might [strength] every day.
Your second sentence is great, though.
Theseus moved the stone easily, took his father’s signs [seals/statues/images] and boldly headed [as you say for “made the trip”] to his father on/by a/the dangerous road.
It wasn’t OCRd for sure, believe me. Book is from year when only MS DOS existed. 
For cottidic I agree it’s a typo in book.
But for adulesceme I am not sure since it’s big difference between “m” and “nt” in “adulesceme” and “adulescente”.
Why did you said “more then enough” for “satis” instead of just “enough”?
Maybe I could’ve put “plenty of strength”, “big strength” or similar.
"it’s big difference between “m” and “nt” in “adulesceme” and “adulescente”
Not really. Often you find such a mistake in manuscripts “m” = “in” = “ni” = “nt”.
Minimè. Saepè tale vitium manuscriptis invenitur.
Why did you said “more then enough” for “satis” instead of just “enough”?
No. It’s “iam satis” = “more than enough”, for an idiomatic translation in English. It’s idiomatic.
Idioma est.
That’s fine with me.