If the value of bitcoin goes up relative to the local currency (CHF, EUR, USD), then when you pay next month, the amount of BTC you'll need to pay will be lower.
They are going to charge you whatever amount of bitcoin gives them X CHF per month. If bitcoin doubles in value relative to CHF, then next month you'll probably be asked to pay half as much bitcoin.
This is no different than if you were buying service from a foreign company, and that company charged you in their local currency. You would have to pay the current equivalent in your local currency. Sometimes you would pay more than last month, sometimes less.
Nobody does. And this is the problem with having no inflation. Every economy needs a slight inflation, otherwise people stop consuming, instead save all their money and it gets worse => deflation.
Bitcoin equals gold, nobody uses Bitcoin to consume anything. I don't know which human behavior you refer to.
Your argument is:
"Why would anyone spend any money if it's worth tomorrow?!"
to support a pro-inflation argument
The counterargument / parallel reality in an inflationary world is:
"Why would anyone accept any money if it's worth less tomorrow?!"
The only difference between the two paradigms is that in the later, the currency creators have the power and in the former, the currency owners have the power. It is no coincidence that the financial institution has chosen to be in control of inflation and extract the wealth first, via seignorage, of currency inflation.
The current price of Bitcoin is the market's best prediction of the present value of holding a bitcoin. When you spend $20 worth of bitcoin, you lose an expected $20 worth of utility from holding bitcoin (and, presumably, gain at least $20 of expected subjective utility from whatever you're buying). The past price of Bitcoin has no bearing on a rational actor's willingness to use it as a medium of exchange.
They are going to charge you whatever amount of bitcoin gives them X CHF per month. If bitcoin doubles in value relative to CHF, then next month you'll probably be asked to pay half as much bitcoin.
This is no different than if you were buying service from a foreign company, and that company charged you in their local currency. You would have to pay the current equivalent in your local currency. Sometimes you would pay more than last month, sometimes less.