1. The USD rallies some during a crisis because it's the USD but against other currencies outside of the Euro, it may not rally much if any. Of course it will rally against the Euro, but unless you are buying goods from Europe that may not impact your life much. The Swiss franc, currently pegged, the euro, would greatly increase in value if the peg was dropped (more so than the dollar IMO). The dollar's relationship with bonds/stocks is not nearly as direct as people think. I would not assume a stronger dollar vs the euro would have a meaningful effect either way.
2. We are still seeing very low inflation in most categories. This has more to do with real estate and domestic velocity of money/other macro points than the dollar.
3. Fed doesn't "print" much money; this is a misnomer. They primarily swap assets and extend lines of credit. This can* cause inflation if improperly handled but the velocity of money is so low it's very difficult to induce inflation. A simple and relevant example is loaning a bank with a strong balance sheet an extra 100m dollars that does not want to lend. The money sits in a bank account. If the fed had given them 10 trillion dollars - and all it did was sit in a bank account - there would be zero inflation. Many firms simply returned the money the fed lent out.
4. Deflation makes growth extremely difficult but it doesn't necessarily have to get to a depression. Someone would have to severely miss manage the economy/government for that to happen (which is certainly possible, if not somewhat likely). We'll hit our wall when our interest rates rise and we are unable to respond. This 'unlikely' scenario is happening all over Europe and will soon spread to Japan.
