Water – What kind of sealant to use by foundation

It is not so much about mortar as it is about the working process. You should clean out the old crumbling mortar to make place for the new one. Remove the old mortar so that all parts are firm and nothing is crumbling - you can even scratch out a bit of the old mortar. The very important part is to wash the wall properly with water so that all parts hold firm and there is no dust - otherwise the new mortar would just fall out. Than press the new mortar in the joints and fill them, make them smooth on surface.

As for the mortar the lime content should not be important for the lifetime, but you can add a bit for better workability. Generally there should be no or very little lime in a stone wall. The new mortar should consist of 1 part of portland cement and 2-3 parts of sand.

If you do it properly (well prepared surface, good mortar), the new mortar should not crumble or dust for tens of years.

A personal experience: it is a very time consuming monotonous work, but the result can be very good if done with care.

An 1/8 inch crack that is weeping water is a fairly serious fault. Wondering, is the crack displaced or flat? Regardless, any crack that allows water to seep through means the crack if through the entire wall. Normally I would recommend chiseling a "key" or an inverted "V" into the concrete and patching it with expanding hydrolic cement and coating the crack with a waterproofing rated for up to 4 PSI. I personally have never used the product you linked to. What is important is that bonds soundly. I would think it might be worth a try since you intend to do a better fix from the exterior in the spring. Remember, a simple concrete pad ove the area will not fix your problem, the leak is ground water, not a little ice melting on the top of the ground.