Interesting question and some very astute comments. I will merge in some of the comments and weave them together to present an answer.
My girlfriend told me that she will write me a letter to provide in
the application that she will be depressed and it would affect her
work if we didn't meet this year because it's been two years since
last time we met.
This idea is nothing short of catastrophic. Full-on disastrous. It totally undermines your claim to having a genuine relationship. While some couples may indeed be apart for two years due to military duty or similar obligations, the normal pattern is that people in a genuine relationship will find a way to maintain the relationship at intervals of 4 - 6 months, or a year at the max. So it leaves you in the awkward position of either being addicted to cybersex over Skype or having to contrive a plausible explanation to answer the question: What has prevented your gf from visiting you in Egypt for two years?
And we have a comment from mkennedy (to whom thanks)...
Based on other answers, a person stating that he or she will make the
visitor leave / follow the visa requirements is discounted, because
most people won't actually do it.
According to anecdotal histories, the only time a gf/bf turns in a bf/gf who is in breach is when the relationship has turned sour and they are looking for some type of vengeance. UKVI believe the common pattern is that friends and relatives do not turn the person in to the authorities, instead they assist in harbouring the person.
There's another relevant comment from Michael Hampton (to whom thanks)...
The only thing that your girlfriend should send is proof that you are
allowed to stay at her house.
If she does not own the premises, then it should be an attestation from the landlord or a relevant clause in the tenancy agreement. She also needs to show that she will be in the UK during the entire visit. They are entitled to refuse on these grounds alone if they cannot find another reason. They can be show-stoppers in their own right.
User DJClayworth (to whom thanks) asks the question...
Is your girlfriend genuinely depressed?
Nice one! So she will include a diagnosis from the NHS defining her condition and her treatment regime? Otherwise disaster looms when a sponsor attempts to elicit sympathy or some sort of human rights claim. It's a credibility hit.
User phoog (to whom thanks) puts a nice capstone on the whole issue of what the gf needs to do...
Above all, you should not include a letter from your girlfriend and a
statement that her letter is "fake." That could get you banned for
deception. It seems to me that the best course of action would be to
omit the letter from your girlfriend altogether.
You also wrote...
I will be sponsoring myself as I work full-time job, I have properties
as my own flat and other family properties.
They do not care about properties; there are tons of Brits who own properties abroad without ever visiting the locale. Local agents collect rent and make transmittals to the owner. Owning property doesn't help your case.
My own comment is that your narrative reads like someone who does not qualify as a family member under Appendix FM seeks to enter as a visitor and then go underground. And the best odds are that they will see it like that also and refuse under Appendix V 4.2 (a)+(c).
In the absence of hard evidence, they will revert to whatever 'pattern' seems apparent. In this case it's to circumvent the financial hurdles imposed by Appendix FM (link above).
Your other question...
The only problem I have is the HR letter I get from the employer is
that it shows no salary section (how much I make per month) as in part
five it asks about money and I'd have to estimate.
If the application appears credible (not your case at the moment), they will be happy to sync up your employment contract to your bank statements.
General note on the Visa Section in Cairo: it's a great location for young graduates on the ECO track to have their first assignment abroad. As a counter-weight, they have a huge battery of local hires (on track for a British passport for service to the Crown) who will verify everything. Upstairs, downstairs, under the bed, everything. Plus a cadre of heavy-weight veteran ECO's to act as mentors. Plus about two centuries of rock solid relationships with prominent Egyptian institutions to call upon if needed (see the classic Alexandria Quartet where it's described at length). Underestimate Cairo at your own peril :)