Must one repeat the prayer if the prostration was incorrect due to an attempt to prevent the emission of gas, and is it permissible not to fully bend in bowing for the same reason?

Prayer while resisting the urge to urinate, defecate, or pass wind is prohibited. If you find a time when the gas subsides, allowing you to pray with proper bowing (ruku') and prostration (sujud) and ritual purity (tahara), then you should seek to pray at that time. If the gas only escapes during bowing and prostration, and if it is possible to perform full prostration with proper purity, then you must repeat the prayer that was performed by gesturing (īmā'). Regarding bending in rukū', if you bend sufficiently to touch your knees with your hands, your prayer is valid; otherwise, it is not sufficient. However, if the gas is escaping continuously, then you must perform proper rukū' and sujūd, and perform ablution (wudū') for each prayer, just like someone with incontinence (sals). You should not worry about anything that exits during the prayer. All of this is assuming the reality of what was mentioned; if it is merely obsessive whispers (waswās), then you should ignore them.