I don't know if I can use a symbol that is a bit similar to a trademarked symbol. For example, can I use the Alchemist symbol for philosopher's stone. It is very similar to the symbol of deathly hallows, trademark by Warner Bros. Who decides how much similarity is allowed? Also, some trademarked symbols are just a combination of some basic geometric shapes, that can be just doodled randomly without knowing. Can anything similar can be used? I am not saying copying the symbol, I just can't check the whole list to check if my symbol matches to another. Or is there any site that allows to check that by uploading the symbol?
Under united-states law the question is whether the symbol is likely to be confused with the protected mark by a reasonable person such as a potential purchaser. If the is a dispute, the decision would ultimately be made by a court. Whether the contested symbol is being used on a product of a similar nature will influence the decision. That the symbol for the philosopher's stone is ancient will make it less likely to be held to be a trademark infringement, but it will depend on how it is being used.
Unlike copyright law, US trademark law does not care whether a mark is complex or original, it cares only that it is distinctive and has acquired a secondary meaning, i.e. that people understand it as referring to a particular product or maker of products (or services). If it has, and is being ":used in trade" then it is protect able as a trademark, even if it is just "a combination of some basic geometric shapes". Note that many trademarks would not be copyrightable, the standards are quite different.
Some logos are protected both under copyright law and under trademark law.
Note also that trademarks are normally specific to a type of product or business. One could set up "Apple Restaurant" without infringing on the mark of the computer company. Trademarks are also specific to a particular country -- what is protected as a trademark in the US will not be protected in Canada, or the UK, or the EU unless it separately qualifies for protection under the laws of each individual country (for the EU, a union-wide trademark is possible). Moreover, a trademark may be limited to a particular region of a country if that is the market in which it is being used, depending on the law of the particular country.
The above answer focuses on the law of the United States. The laws in other countries are similar in outline, but significantly different in detail. For one thing, in the US a trademark may be established by simply using it, although additional rights are gained by registration. However, in many countries, there is no protection without registration.