What can a lower house majority of the National Assembly do without an overall majority?

My understanding is that the establishment side only needs 126 seats in the lower house, which they will have, to combine with their 250 seats in the upper house for a majority. While the opposition (red+orange) would need 376 seats in the lower house, which they will not have, to overcome the establishment’s 250 seats in the upper house for an overall majority.

The opposition will have a majority in the lower house but not overall. So what can they do with that? For example they can not elect a Prime Minister, the establishment can. Can they form a government?

The inverse question is also relevant. What can the establishment side do with an overall majority but no majority in the lower house? They can elect a Prime Minister. Can they form a government?

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