The client can still write their content using the pronoun 'I'. Your copywriters could adjust that content using pronouns such as 'they', and then see if your client prefers the amended content.

Personally, I think readers of content written in the first person are less likely to trust and like what is being conveyed. A person or company that talks about themselves is much less credible than that person or company being talked about by someone else. Show your clients examples of first-person writing vs. third-person writing and see which they prefer. As you say, client is boss.

It would tend to indicate that users are less engaged with your site. More visitors, but they are looking at less stuff on your site. This suggests that users aren't getting what they are looking for when they come to your pages. Perhaps it is time for a keyword rethink? If not, then assess your content. Would you find it useful? Also, look at where you are most visible and see how relevant you are to the audience that will see you there.

Using bold, underline and italic is fine. As long as there is a purpose, you will not be penalised. Remember the golden rule, be natural. If it is necessary to underline a keyword, then do so, but don't do it just to optimise that keyword..