First let's take a look at the reasons for your refusal...
You correctly stated that you are a student, however your studies end soon and no explanation is given on your future plans. Therefore your occupation is unclear.
You have provided a bank statement with a large enough sum, however unexplained deposits of large sums were recently made, which casts doubt that the funds are actually available to you.
The consular officer is therefore not satisfied that your ties to your current place of residency are strong enough.
Now to answer your questions...
As I intend to reapply, with evidence showing that my studies extend to the end of the year, and with proof of my earnings (payslip) in the last six months which showed I earn more that 3,900 as well as my part time job contract which were not included in my previous application, what are my chances?
That will certainly be a good improvement. However make sure to follow our recommendations for bank statements, particularly avoiding painting a picture of 'funds parking'. Given your German residency permit your odds should be good to begin with.
Does this mean I now have a change of circumstance?
A change of circumstance at the deepest level means your ties to your home country have become stronger. This might include:
- Well-paying job that you've occupied for a couple of years
- Real estate in your home country, possibly with a mortgage
- Strong family ties, such as marriage and/or children
- Successful business that requires your physical presence
- A residency permit in a high-HDI country (you already have this one)
If you reapply immediately, you will instead be providing compelling new evidence (using UK visa refusal terminology), rather than a change of circumstance. This means that your circumstances have stayed exactly the same, but you believe they are sufficient for receiving a UK visa and the only thing missing is evidence of those circumstances.
Is it wise to use an invitation letter reapplying?
An invitation letter might demonstrate that you have definite plans for your visit or that someone else is paying for your trip, but that alone is not sufficient. The consulate wants to see your ties to your place of residency, not just that someone else wants to see you in the UK. Unless an invitation letter is expected (e.g. you're going to an academic conference), I wouldn't rely on it to improve my odds.
Is it wise to reapply after one month of refusal?
This one is up to you. If you do reapply, make sure to include a good cover letter explaining your personal circumstances and trip plan in succinct detail, as well as what changed since your previous application. Overall our advice here on TSE is to wait for some time and collect new evidence of your ties, rather than rushing to reapply and risking a second refusal.
On a final note, please make sure to return to this site and update us on how your application went through (if you do reapply), as this will be very helpful to future visitors.