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If the e-mail is basically "complete" with subject line and attachment such as your example then I might add "see attached" or something but there's really no point in bulking the e-mail out with "fluff". They want the attachment - they get the attachment and use it. Job done.

Random quotes from the internet will just make you look immature - not that it will be a big deal though since people probably won't read them.

 Hi bracco23,

please see my answer in the attachment.

Greetings, Chris

There is no reason to bloat your email with unnecessary text. These
people will handle a huge bunch of those emails, you will disturb their
workflow if you keep adding noise.

Also your boss might not get offended by your random quotes, but he
might get offended because your browsing the internet for useless
stuff.

Keep it short and simple.

Informality and unrelated content in work messages are not professional. That does not make it unprofessional.

When this is acceptable and when it isn't is very nuanced, and depends on the office culture, the audience, how often you do it, how well it is received, your particular relationship with everyone who will see it, your reputation, your age, etc. Generally, if it in any way impedes business functioning the only professional response is to stop.

People who have these social skills are more popular, more influential, and can see concrete advantages in their careers.

Is it professional to write unrelated content in an almost-emtpy email?

No. Why would you confuse the reader by adding something random?

Try to keep it short and simple.

There's no reason or need to "adorn" the email with superfluous text. There's also no reason to write the same thing in the email as is contained in the attached time sheet.

Attached is my time sheet for the period xx/xx/xxxx through
xx/xx/xxxx. Thank you.

The random quotes probably are of no benefit to the recipient, the people who choose accounting like staring at numbers all day, they don't need a surprise package from the real world, if they need a break they can go to the water cooler, stare out the window, make some paper airplanes, etc when they are ready for it.

Stating your name again in the email is probably not needed it's already in the from header and in the signature at the base, the date also is not needed.

The summary is also not needed, but it is not without merit. having a precis there (like say just the total hours) could help with resolving disputes in a timely manner eg if the attachment is hard to read or if there is a misunderstanding, and they notice that your number does not match the time-sheet you could find out and resolve it before pay-day.

If you are submitting the timesheet late, having the date could be useful to help you find the email at a later time should you need to. So having the date in the subject line on late submissions could be useful.

This really depends on your client company. I've seen different companys. In some of them (mostly young and related to creativity), people would do funny things, play jokes on each others (and also on their clients, but they never crosses a line), use "4-letter-words" in their day-to-day-language - things which on this site would not be seen as professional. In others, those things could be your death sentence (not literally).

So, I would suggest you to take a look on them. How do they speak? How do they write? How "funny" are they and how serious is work for them? Are they like the members of this Stack Exchange site? I think those questions may help you evaluating what to do.

As many have said unrelated information is not needed. If you state the time period that is fine, because it can let them see at a glance which time period without having to open the attachment.

Putting the time period in the subject can be a big help help also. Not only can they find the appropriate email it can also help to avoid the situation where the email software tries to group all the email messages that have the simple subject such "timecard" into one conversation.

The worst situation is to only have fluff and no other useful information. You might be training them to always skip reading the short emails because they believe they always only have fluff.

Always include a signature block with all your expected contact information.