Language has several different elements to it. Listening, writing, reading, speaking, etc. Shadowing will strengthen listening and pronunciation, but that alone will not give you fluency. It is important to develop other elements of a language as well such as writing and speaking. While you may learn some new words doing shadowing you will need to understand grammar principles to apply them and increase your fluency. One last comment I would make is to be aware that many speakers on TED talks speak with different accents. People from all over the world are speaking in English and some of them mispronounce words so be careful with which speakers you shadow. I wish you the best.

1) No it does not sound strange to use "have" in that way. Hearing a company say "We can have a specialist come out to meet with you," or "We can have someone help you," is actually quite common. 2) Those phrases are not odd and will be easily understood by a native English speaker. 3) Each of those words can describe a nurse giving you shots. The difference between them is the force applied. If the nurse was rougher when she gave the shot you might say she "jabbed" you. If the shot is simply administered often people will say "poked" because it is a lighter sounding word. "Feeling some pin pricks" works for describing the sensation of feeling the needles of shots going in. You can also describe certain sensations that might accompany the shot. For example: stinging sensation, sharp pain, etc.