If the custom of that land is that the best adornment is to cover the head or to pray in a garment with full sleeves, then praying when one is dressed as mentioned in the question is contrary to what Allah has enjoined, even if the prayer itself is valid. But if the custom of the people in that country is to dress as described in the question, then there is nothing wrong with praying dressed in this manner.

It is not permissible for a woman when praying to wear tight clothes that forms her `Awrah such as pants or trousers. Even if a woman goes against this ruling and prays wearing these tight clothes, her prayer is still valid, because what is required is to cover the `Awrah, and she has done that.

Although the chest is not part of the ‘awrah for men, uncovering it is still an action that is not appropriate for a man and is one of the actions of the immoral.