I think the answers are situational, but some rules of thumb:
A. For first, or early dates, where typically both parties are getting to know each other and see if mutual interest develops, I tried to avoid any big expense date activities. Meaning, if the prospective date suggested a expensive dinner, or event with pricey tickets, I suggested more casual dining or an alternate activity, and would acknowledge I was open to time together to get to know each other. I agree it is considerate to avoid, as possible, someone making an unreciprocated emotional investment, and think it extends to financial investments, too.
B. I often accepted a date as offered, and acknowledged it as an opportunity to get to know each other better. I generally intended that as recognizing we did not know enough yet to ascertain our respective level of interest, but in hindsight, years removed from dating, I am just now seeing that it could be taken by some to mean "I cannot wait to know you more intimately.". So, if I were to be in a dating situation again, I would be more careful in how, or if, I expressed that thought.
As for the whole "give them a chance thing.". Ugh. That might be a reasonable reply to someone who has stated uncertainty of their own interest in another, or maybe if someone is bemoaning a lack of dating prospects while also stating they have declined recent invitations, but beyond that, i think it best to recognize other's ability to reach a decision as to how and who they choose to date, and I would not generally question it.
I remember getting that comment after describing to a friend a date I did not care to see further and thinking "I did give him a chance, and dating isn't a contest, so once I have a firm opinion this will not lead to romance, it isn't open for others votes."