Inflation actually tends to benefit the poor in the long run, as it devalues debt. (By definition, the poor don't have a lot of savings and tend to be in debt). Hyperinflation of course causes problems for everyone, but that's not going to happen. That said, there's little reason to worry about out of control inflation for several years to come: these economies still have enormous under-utilized resources.
No. The poor are typically in debt on short-term scales (days, weeks) which does not benefit from inflation, and at rates (often double digits) which inflation does not mitigate.
The rich are typically in debt a lot, via leveraged investment ('trading on margin'), or, indirectly by things like leveraged ETFs, leveraged currency FX trading, etc, which enjoy very low, bank-level interest rates because it's done in bulk. Not to mention banks with direct access to low-interest loans, (as in bank corporations) which are not begging in the streets for alms (they get bailouts). These debts that the rich enjoy benefit greatly from inflationary devaluation of nominal prices.
Moreover, the investment activity of the rich tends to benefit from inflation.
While I'm sure there are some rich that are heavily leveraged, the majority are not leveraged that highly relative to their asset base. This has been shown in most available statistics on household wealth. For example:
In particular the debt-equity ratio of the top 1% (>$8.2m net worth) is 2.8% ; the next 19% (> $473k < $8.2m) is 12.1%, and the middle three quintiles ($200 dollars-$480k) is is 61.1%.
Moreover, the rich representatives in press & politics (WSJ editorial page, Forbes, the GOP, etc.) have been clamouring to raise interest rates for the past 5 years out of inflation fears... for what reason? To benefit the poor?