We sent our advisor a document giving 100 shares as a "thank you" for agreeing to help us for free. Should we stop including stock in all our advisor agreements?

Most of the people you’re reaching out to won’t be this sophisticated. We say to offer shares as token equity, but if they have a conflict or don’t want it, then no need to include it.
Signing advisory agreements depends on engagement level. Is this someone part of your “greater advisory board” or is this an active advisor you’re meeting on a regular cadence. Legally, if the person is actively helping you draft sales material / other content that customers may see or have access to any data, you could get in trouble if no agreement is in place due to IP assignment, disclosure of info, etc. Yet need to trade something of value for the contract to be legitimate (in the usual case: shares or options). That amount has a very large range and is somewhat dependent on the sophistication level of the advisor as Danielle mentioned along with involvement levels. Have they been a founder before, made a large exit, have they made angel investments, are they in Silicon Valley vs working in a more traditional industry in another city. The typical start up is incorporated with 10M authorized shares, so some can do the math.
You can also tell them that you can do it the formal or informal way. Informal meant they agreed to 3 calls over a month or so. By the 3rd call it was very clear to both parties whether or not this was worth pursuing with a formal agreement.