1. Not sure what you mean by "milk of water kefir"--water kefir grains are different and produce different strains of beneficial bacteria, and to a lesser extent yeasts. Personally, water kefir did not help me, but it tastes awesome if you do a secondary ferment with juice and a bit of sugar to prime the bottles. I drank it everyday, because I wasn't sure how long to keep the grains inactive but alive--like in an airtight water/sugar solution in the fridge which you let breathe every few days. I haven't tried my water kefir grains for over a month; they have been stored as described. Overall, drinking it daily may have upset my stomach a bit, so I quit and got milk kefir grains--much better for ME.
With water kefir: I mixed sugar water, a few tablespoons of ginger medalions (cut like coins to make straining from grains easier), some minerals (like a hard boiled egg shell), maybe a couple tablespoons of dried fruit (not necessary), and a quater inch slice of lemon. I'm going from memory, but youtube it. I think I did a day for each fermentation, one with grains and ingredients above and another day in sealed bottles with a fourth cup 100% juice and a half teaspoon of organic cane sugar.
With milk kefir: I simply buy 2% organic milk and put a cup per tablespoon of grains and let sit for two days. Then strain and repeat. Ideally you'll grow your grains to make enough to perpetually supply yourself a two day supply for your needs. I mix: banana, chia, shelled hempseed, raw cacao powder, and stevia in blender with kefir milk. *Note: homemade kefir is not the same consistency or taste as store bought. It should, in my experience with whole milk which separated to curds and whey too much, be done with 2% milk, but that is my personal preference (as is the funky recipe above, just mix it with something). You could possibly just mix a 10 oz glass of kefir with 10 drops of vanilla stevia, to simplify it.
2. I have 1-2 smoothies a day, and it is awesome. I am addicted. Prior to this homemade stuff, I gave up on the store bought which isn't as probiotic rich and gave me a slight bloating feeling. Mind you, I still take copious amounts of probiotics otherwise, like a dose a morning/afternoon/night. Homemade kefir never causes me bloating or any problems whatsoever. I haven't experimented eating the actual milk kefir grains, as a source of potent probiotics. I have read of people who blend a bit up with their smoothies, but I didn't have enough to experiment with this...until now. Thanks for reminding me. I'll let you know if I do it and experience anything good/bad.
3. Um, not sure what you mean either. If your doctor is experienced with using specific antibiotics for specifics aims, and has proven track record, then it is up to you and your doctor. Yes, I have heard that this can help some people in certain circumstances which I am, unfortunately not fully informed of. If you must take antibiotics, then, yes, if it were me, I would definitely take some form of probiotics a couple hours after the antibiotics. Personally, kefir alone is not strong enough--maybe if I had 3 smoothies a day...but I haven't experimented and this is largely an individualistic thing for you to decide.