Is it permissible to offer mandatory prayer while sitting?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions. Standing up is a pillar in the mandatory prayer and the prayer is not valid without it unless one cannot do it. As for Nafila (supererogatory prayer), one can perform it in the state of sitting even if he/she can stand, but his/her reward is half the reward of the person who prays while standing if he/sh has no legal excuse for such an act. And Allah Knows Best.
Is it true that whatever is dry is pure even if there was impurity on it?
The impure material object does not soil (make impure) anything else unless the impurity is wet and transferable. But, if the impurity is dry or non-transferable, then there is no problem. Fuqaha has stated that: There is no disagreement between Muslim scholars that when a dry impurity touches something dry it does not make the latter impure.
Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
We collect funds from mosques and other sources, saying: "For the poor, the needy, widows, orphans, and those who do not beg insistently." After paying the stipends of the families registered with the Zakat Committee, an amount exceeding 6,000 dinars remained. Is it permissible for me to save it for upcoming months when I may not be able to collect the stipends?
These funds are received by the committee as representatives of the zakat payers to deliver zakat to those entitled to it. It is well-known that delaying zakat while being able to pay it is not permissible. Imam Al-Nawawi (may Allah have mercy on him) said: "Zakat must be paid immediately if one is able to do so, by the presence of wealth and the eligible categories." [Al-Minhaj] Therefore, the committee must distribute the zakat to the eligible recipients without installment payments or using it to purchase material goods for them, as the committee does not have authority over the poor to allocate it in this way. And Allah Knows Best.