In terms of software, I use Beersmith. Its competitor, Brewer's Friend, has a reputation for being very user friendly and subsequently is gaining market share. I've mucked around with Brewer's Friend and think it's a bit of a toy, but reasonable brewers can reasonably disagree about that point. Personally, I prefer Beersmith because I think it's a much more powerful tool, but it takes more effort to get it running. I coach new brewers with some regularity and I steer them toward Beersmith because it forces them to really learn their systems. It's painful at first, but it quickly pays dividends. That said, they're both quite good. You can't go wrong with either--but it should be noted that Beersmith is written for and used by actual breweries. But I suppose Brewer's Friend has been around long enough that I'm sure there are a few breweries that use it.
The dry run with water does not include the mash, that simply establishes your boil off rate. To do that, you use a trusted vessel/method to place your target pre-boil volume into the kettle. You then boil for your target time, then cool the water to ~room temp and measure the difference. You then plug those numbers into your software and you have a raw approximation of your boil off rate. That's a big help, it allows your software to figure out what your pre-boil gravity needs to be to achieve your target post-boil gravity. In turn, this allows your software to predict the amount of malt you'll need to achieve your target OG. This is good because, as a new brewer, the bulk of your inefficiencies will be found in your mash tun and it will allow you to focus your efforts toward becoming more efficient on that critical point. Going forward you're going to spend the bulk of your time trying to figure out why your pre-boil gravity/volume doesn't match your predicted pre-boil gravity/volume. Once you have that sorted, you're actually brewing. To isolate that, though, you first have to establish your boil off rate. Everything is connected and it's infuriatingly complicated--get used to it.
Regarding your strike (that is, mixing your grains with water), don't worry too much about high heat while you're striking. Yeah, you're going to kill a few enzymes, but you'll have more than enough available to get the job done. You don't need to worry about that unless you wildly overshoot your mash temp--160F+. Just keep gently stirring. The more you keep mixing the water with the grist, the more even the heat transfer will be. There's a lot more to it than that, and many more techniques, but you'll be fine if you just do it slow and keep stirring. Back in the olden days I used to heat up my strike volume to ~180F and literally just dumped it into my mash tun, then started stirring. Frankly, I'd never do that today! But I made some rather pasable beer with that butcherous technique. Just remember, the malt desperately wants to become beer and you've gotta really screw the pooch to keep that from happening. Whatever you're doing is likely perfectly fine.
Lastly, here are a few screenshots of the data I collect in my Beersmith notes tab--I appologize about any naughty language, but this is my mind while brewing. My primary concerns revolve around pH, gravity, and volume. My system is very much dialed in, so my notes are quite short. As a beginning brewer, you might have a lot more to say. Mark any questions you have, mark any frustrations you may have, and certainly congratulate yourself for any triumphs you achieve! It's a slow, frustrating hobby. Be certain to celebrate your wins, no matter how small!
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I hope you found that useful, feel free to hit me up if you have further questions.
Stick with it! It's worth it.