"Fixed" vs "fixes" when things are already done

If you’re saying what you did today, then fixed bug is fine. If you’re saying what you’re doing tomorrow, it would be normal to write fix bug, as a note, in imperative form, to remind yourself and others what you’ll be doing.

A 'daily report', technically, can only contain what you did that day. If you include what you are going to do tomorrow, it's a plan, not a report. So for the bug in the logout page, you should say 'fix bug'.
"Today's bug" (eg in the login page) is ambiguous, depending on whether the fix is before or after the report. If you fixed it in the morning and write the report in the afternoon, 'fixed bug' is fine. If you are in the middle of the job, say 'fixing bug'. If you are planning to get to it later today, say 'fix bug' again, or (for clarity) 'will fix bug'.

If you are speaking of yourself as the agent, it would never be appropriate to use the third person ("fixes a bug"). If you are speaking of your work, it is not wrong to use the present tense to describe what it accomplishes.

A simple Google search for "this release fixes a bug" returns close to three million results in which the present tense is used to describe an activity that has already occurred. (N.B. The corresponding search for "this release fixed a bug" turns up a mere 800,000 entries.)

Remember that the present tense is also used to describe an ongoing condition or continuing state (see How do the English tenses correspond temporally to each other).

Using the present tense is appropriate here, and, curiously, using the past tense would possibly cast doubt on the accomplishment (which may be why the Google search for the past-tense construction turns up so relatively few hits). If I say "this release fixed a bug" it might imply that the fix was no longer successful, and something came along which counteracted it.