It is possible to install the Chrome Browser on the Kindle Fire HD but you have to jump thru a few hoops to do it (do a web search on side loading apps). The weakest link in the Kindle Fire HD is the fact that you only have access to the Kindle App store which is only a subset of the much larger Google Play Store.
The Kindle Fire HD comes with a charging cable that can be used to plug into USB ports on wall warts, laptops, etc... but some ports may not supply enough current to charge or may charge slowly. You can buy a charger that works with the cable for an extra $20. I would just figure in that extra cost.