Is there any halachic issue with lying on websites? For example, if a site requires you to be 21 and asks, “Are you over 21?” And you're not, but select “yes”. Is there any problem with doing so?
I think this article will give insight into possible answers to you questions.
Generally, one should avoid lying as the Torah instructs (Shemos 23:7), מִדְּבַר שֶׁקֶר תִּרְחָק.
Yet, there are exceptions when for a purpose. For example, (from that article):
One who is shipping fragile objects such as matzah can write the word "glass" on the box in order that it should be dealt with properly. (But it is better to simply write "fragile".
See also, this article.
It seems that the lenient view would allow answering "yes" on such a site if it will not cause anyone a loss. The more strict approach would prohibit it even if it causes no loss (so as not to express a bad trait of dishonesty), unless there is a specific benefit that outweighs this concern, such as to protect someone's dignity.