Is it Islamically obligatory to pay the deferred mahr (dowry), the 'mut'ah' (consolatory gift) and to buy a new gold set and provide financial guarantees to the ex-wife in order to take her back? And what is the ruling on paying a mahr and buying a new gold set with financial restrictions to take her back after divorce?

You must pay the remaining deferred mahr (dowry) that is due to your wife immediately upon its due date, unless she waives it. You are not obligated to pay the mut'ah (consolation gift) according to the more preponderant opinion, but paying it is preferable, and its amount is determined by the husband's capacity. You are not obligated to pay maintenance for the iddah (definition) (waiting period) because she has become irrevocably divorced from you, and an irrevocably divorced woman is not entitled to maintenance or lodging, according to the majority of scholars. There is no objection to what she stipulates for you anew at the second marriage contract, such as a shabakah (engagement gift) or a specific mahr. If you accept it and commit to it, then you must fulfill it. However, you are not obligated to commit to it; rather, you can negotiate with her and involve righteous people as mediators to lighten the conditions. The previous marriage has ended, and what you will undertake now is a new contract, like an initial contract, with all its conditions and pillars.