It seems that all this could be avoided if the addresses started with the symbol to identify the correct currency or at least the beginning of each currency should always be different than other currencies. This seems like a major flaw in the system.
There is no "the system". Each cryptocurrency creator can choose how to represent an "address"; there are no rules that they need to follow nor is there anything to enforce the altcoin creators follow certain rules. Yes it would be nice if all addresses for different currencies used different prefixes, but there are not enough characters (at least characters that most people are able to type) and sometimes altcoin creators aren't smart enough to realize that that has to be done.
As for the rest of the long address, are you saying that it would be exactly the same the entire long wallet address from start to finish?
No, the rest of the address will be different. This is because the prefix character is not a character that is appended to the beginning of an encoded address (which is why using a currency symbol won't work). Rather it is a specific byte that is appended to a hash that happens to result in a specific character when encoded in Base58 (which is the base/alphabet that most altcoins use for addresses because that is what Bitcoin uses). That byte is a version byte and it is also hashed along with the actual data for a checksum that is appended to the end of the encoded data. This whole process is called Base 58 Check Encoding; google it.
So to use a home address analogy, would sending a bitcoin to a bitcoin cash address be like sending something to your correct house address but having the wrong name on the person or would be be like sending something to your address with the correct street number,street name, city, however putting the wrong state or country.
More like the latter where a different countries are like different coins.
I am trying to find if my online bitcoin only wallet which address I copied and pasted exactly has the bitcoin cash that was deposited to it. (bitcoin vs bitcoin cash) or if the address belongs to someone who holds an identical address for bitcoin cash on another system. (Same phone number but different area code)?
The address belongs to you and whoever holds your private key. Private keys and addresses have a one-to-one relationship (well almost). The private key corresponds to a public key and the public key corresponds to the address. Your address on the Bitcoin Cash network could belong to someone else, but it also belongs to you. If it belonged to someone else, then they also can control your Bitcoin that is associated with that address. Whoever has access to the private key for your address has control over the Bitcoin/Bitcoin Cash/whatever altcoin it is associated with. Private keys can work across multiple altcoins because it is just a 256 bit number that is used as an ECDSA private key. The address and its prefix doesn't matter; that's just an encoding for the data.