لا يمكنني تحمل ذلك

Not necessarily. It depends on your tone. It is a direct expression of a limit. In a professional setting, it's better to use 'هذا فوق طاقتي' (This is beyond my capacity).

Yes, but it's more common to use 'لا يمكنني حمل هذا' (I can't carry this). 'Taḥammul' implies the *effort* of enduring the weight over time.

'Astaṭī'u' is about your internal ability. 'Yumkinunī' is about whether the situation allows it. In this phrase, 'yumkinunī' is the standard idiomatic choice.

You would say 'لا يمكنني تحمله' (Lā yumkinunī taḥammuluhu).

In dialects, yes. 'ما بقدر' (Mā bi'dar) or 'مش قادر' (Mish 'ādir) are much shorter and very common.

Yes, it is perfectly acceptable in formal writing to describe social or economic pressures.

It's a demonstrative pronoun meaning 'that.' It refers to whatever situation or thing you were just talking about.

Arabic verbs use object suffixes (-nī) to show who the action 'is possible for.' 'Yumkinu ana' is grammatically incorrect.

The root and the concept are, but this specific modern phrasing is more common in Modern Standard Arabic.

Yes: 'لا يمكنني تحمل رؤيتك هكذا'. It's a very common way to show deep concern.