Ben zamanı iyi kullanmakta zorlanıyorum.

-makta is the locative case applied to the infinitive kullanmak (“to use”), literally meaning “in using.” Turkish often expresses “having difficulty doing X” with this pattern:
• infinitive (kullanmak) + locative -ta/-te → kullanmakta (“in using”)
• kullanmakta + zorlanmak → “to have difficulty in using.”

zorlanmak is an intransitive verb meaning “to struggle,” “to have difficulty,” or “to be strained.” It doesn’t take a direct object. Instead you say what you struggle with by using an infinitive in the locative:
• yemek yapmakta zorlanıyorum – “I’m having difficulty in cooking.”
• kullanmakta zorlanıyorum – “I’m having difficulty in using…”

No. Turkish verbs carry person/number information in their endings. -yorum already indicates “I” and present tense, so you can drop Ben:
• Zamanı iyi kullanmakta zorlanıyorum.

You can use the negative potential of kullanmak:
• Zamanı iyi kullanamıyorum.
That means “I can’t use time well.”
Nuance:
– kullanmakta zorlanıyorum emphasizes the ongoing struggle.
– kullanamıyorum states inability more directly.

Yes. Replace kullanmak with the verbal noun kullanma + locative -da:
• Zamanı iyi kullanmada zorlanıyorum.
Both sentences are correct; kullanmakta vs. kullanmada just use infinitive vs. verbal noun.

Both try to express “having difficulty while using time,” but they use different gerund forms:
• kullanmakta – infinitive + locative (“in using”)
• kullanırken – adverbial participle (“when/while using”)
In practice, kullanmakta zorlanıyorum is more idiomatic for zorlanmak. kullanırken zorlanıyorum sounds a bit awkward because “using time” isn’t a momentary action you’re “in the middle of” in the same way you say yürürken zorlanıyorum (“I struggle while walking”).