score:10
Your sister will not be visiting the UK for your birthday this year, and quite likely next year also.
The first paragraph of your refusal explains that while your sister nominally submitted the correct documents, their quality was such that they had no evidential value. He noted that an endors*m*nt from a chartered accountant is of no value if the tax returns are self-prepared. As a result, the ECO dismissed all of the financial evidence.
The second paragraph informs us that your sister's prior visa was curtailed (a bad thing), and that she worked in breach of conditions (a bad thing), and that she overstayed her curtailment (a very, very bad thing). The ECO dismissed her reason for overstaying as invalid because illness has a lawful procedure and your sister did not (apparently) use it.
As a consequence, the ECO determined that your sister did not qualify. This is consistent with the notion that people who abuse their visas will have a difficult time going forward. Your sister prevented a mandatory ban by leaving voluntarily, but they are obliged to consider the applicant's history and credibility regardless if a ban is in effect or not.
Your observation that she left before her student visa expired does not work because when a visa is curtailed, it becomes obsolete and the person needs to leave before the curtailment date.
Fixing these types of problems usually takes a long time combined with a substantial change of circumstances.
Finally, for your question about whether she can apply from inside the UK, the answer is no, entry clearance applications must be made outside the UK (Appendix V of the Immigration Rules).