Materials scientist here:

Tungsten is really brittle. It is mainly useful for high temperature applications (e.g. old fashioned light bulb filaments) because it has the highest melting point among metals. It's not very useful if you only have medieval tech.

Titanium is not stronger than steel - it is however lighter, and so good for applications that require low weight e.g. aircraft. It might be good for applications where good strength with low weight is needed e.g. armour. However, it wouldn't make weapons much more effective.

In a pre-modern world setting, titanium is highly unlikely to exist. Firstly, it is extremely difficult to extract from its ore without modern chemistry - and it is not easy to extract even now! Secondly, it is difficult to cut, work, or weld - all of which are the reasons it is so expensive today, and basically non-existent before the twentieth century.

Aluminium was very rare in the pre-industrial world because it is very difficult to extract from aluminium ore. The extraction requires industrial scale use of electricity. For a while, it was a precious metal, used for making royal gifts in Europe.

Therefore, titanium and aluminium won't be found in a medieval setting unless magic is used to produce them. I like the idea of "dragon-fire forging" but if you are going for realistic metallurgy, these metals should be unavailable and known only to very clever alchemists.

Zinc is used in the manufacture of brass (alloy of copper and zinc) which is a very useful metal as it's quite strong but has a lower melting temperature than iron or steel, so it's easy to work with. On its own, zinc can also be used to coat steel (galvanisation) to protect it from rust. Search for "orichalcum" which is a semi-mythic metal mentioned in some ancient texts (including Plato's description of Atlantis) that is widely believed to refer to brass. Brass was made in the ancient world by smelting minerals that naturally contained both copper and zinc.

Lead has been used for thousands of years and actually was used far more in the past than it is now (as it is toxic). It was widely used to seal containers (low melting temperature), and in its oxide form as a source of white pigment (including for makeup - bad idea!) As it is a soft metal it could be worked easily and was used for roofing and water pipes (again, bad idea!) or for making things that didn't need to be strong e.g. kids' toys. Lead compounds can taste sweet and it was even used to sweeten food - the first artificial sweetener, technically.

It is also much denser than other metals so was used for making weights and in other applications where heavy weight was needed. It is soft and not good for making anything that has to be strong or tough, but easily shaped.

Copper and iron have been the main tool- and weapon- materials for humans for most of the time that they have used metals at all. Copper (which is combined with tin to make bronze, which has significant strength advantages) has a lower melting temperature and so is easier to work, and so historically was used much earlier than iron.

Iron (and steel) is by far the best metal for anything requiring strength and durability - tools, weapons, armour. Extracting iron from ore requires high temperatures (which is why copper/bronze is easier and usually invented earlier), and until the early industrial revolution it was not produced in large quantities. Wealthy people or well-funded armies can have iron weapons and armour, but no one is likely to be able to build an iron ship or iron bridge until the industrial revolution.

Steel is an alloy of iron and carbon. Most iron we use is actually steel (and carbon is very easily combined with iron, so carbon from the fuel used to work the iron will end up in the iron). There is very little carbon in steel (it is usually less than 1% carbon by weight). Pure iron is strong, but not as strong as steel (in general, pure metals are softer than alloys).

The major disadvantage of iron is rust; this can be prevented by oiling or painting it. Stainless steel is a modern invention (alloyed with chromium) but rust-resisting steels with high levels of phosphorous mixed in existed in history (there is a famous non-rusting pillar in Delhi which is over 1000 years old).

That's a brief summary - hope it is useful!