This question comes up frequently, and we have some good answers in our FAQ: a short one by u/Rittermeister and a rather more comprehensive overview of the rise of gunpowder weapons (and their merits) by u/Valkine.

While the question has come up and been answered before, as already linked, some comments on some of your specific points:

1. they have a terrible reload time

Not too terrible (20-30s), and similar to crossbows. Given that crossbows were successfully competing with bows on the battlefield, a musket should be able to as well.

2. Are very easy to damage like with water or mud

A matchlock musket is not easy to damage with water/mud. It will get wet/dirty, and can be cleaned. There are few moving parts, and fairly loose tolerances, and it will work when dirty. Wet powder will be a problem, but the gun itself will not be damaged. Modern rifles are precision-made, and have many moving parts that fit closely (tight tolerances), and are much more susceptible to problems when dirty.

Bows can also be damaged by water. Wet bowstrings can perform badly (or just fail). Composite bows can be badly damaged by water (because the glues used can fail).

2. Cheaper and somewhat easier to make

"Cheaper" depends on the bow. A composite bow could be more expensive than a musket. Muskets were similar in price to crossbows, so, again, could be expected to be as competitive as crossbows vs bows.

While wooden self-bows (like the typical longbow) were cheaper, the bow by itself is useless - an archer is needed. According to James P. Ward, "Prices of Weapons and Munitions in Early Sixteenth Century Holland during the Guelder's War", Journal of European Economic History 33(3), 585-619 (2004), a musket cost about 2 days wages for a soldier. The major cost of a force of musketeers or archers was wages and supply, not the initial cost of the weapons.

Let's us address the issue point by point.

What I understand old guns like a musket are not good.

Virtually every commander since late 15th century tends to disagree. We can argue all we can, but the firearms quickly made neurobalistic hand weapons (bows and crossbows) obsolete, so they had to be better in practice. It is as simple as that.

1. they have a terrible reload time

Not really. As u/wotan_weevil already wrote, muzzle-loaded rifle could be loaded in 20-30 seconds, give or take. But see the note about unit firing below.

2. Are very easy to damage like with water or mud

If you don't count a match getting wet, 16th-18th century muzzle-loaders were extremely difficult to damage. They consisted of thick metal barrel and sturdy stock. The weak point was a complex lock, yet this usually applies to wheellocks, but not to early matchlocks (essentially a primitive metal lever with a burning match) or flintlocks (a sturdy hammer assembly, single, thick flat spring and a trigger not unlike the one used in crossbows). Lock was hidden behind well-fitted brass of steel plates, so dropping the gun into the mud was definitely not detrimental. Cleaning the firing pan was usually more than enough.

Bows and especially arrows, on the other hand, are pretty susceptible not only to water but even to humidity. Wet bow of that era was basically useless in combat or hunting, and arrows that got wet could easily warp afterwards ruining accuracy.

3. Some old guns specially flintlock had terrible precision.

Flintlocks were the penultimate stage of firearm development prior to the invention of a cartridge (the intermediary stage was caplock, developed in early 19th century). Also, the type of lock itself has little to none influence on accuracy - early guns were simply too heavy for the lock operation to be even felt. Accuracy boils down to two things: rifling and precision of manufacture. During the American War of Independence (I assume you mean this one, as you speak of 18th century and mention flintlocks that were obsolete in 1861, when the American Civil War broke out) good methods of rifling was already known and manufacture quality was also good, especially in case of hunting rifles.

One account from 1794 states that one of the marksmen in an unit fighting during Kosciuszko's Uprising, when asked to present his skills to a visiting officer, managed to shoot royal monogram (i.e. write royal initials with bullet holes) at 100 paces. And in the context of American War of Independence we have to mention Timothy Murphy, who managed to fatally shoot General Simon Fraser during the Battle of Bemis Heights in 1777. Depending on the source, the shot was taken at 300 to 400 metres. It is virtually impossible to achieve such feat with a bow.

4.they were Somewhat expensive to make at the time.

For an individual (and by extent the local militia) - sure. But for the national manufactories supplying a standing army not necessarily so. This would be and issue in an apocalyptic scenario leading to societal disruption, but not in the historical timeframe we're speaking about.

While during those times bow and arrows had

1. Had a faster reload time

In case of battles this is of relatively no issue. When shooting in formation, shooters follow commands to concentrate fire, and thus the ability to shoot faster is lost to a large extent.

2. Cheaper and somewhat easier to make

It depends. Bows, unlike guns, could have been made at home, using simple tools. But the mass production of guns in the manufactories meant that they could have been made quite quickly. Not to mention that powder and especially bullets can be made quickly, while making arrows is a long process and starts with finding proper material (shafts must be perfectly straight). Production of a high-quality bow is also time-consuming as harvested wood must be seasoned for a long time, sometimes years. Making a composite bow of wood and bone required very specific knowledge and skills that were very rare in 18th century.

3. You Could arch your shots

You can arch any shot. Musket ball falling from above is still pretty dangerous. But if you are able to eliminate your enemy at 400 meters (or over a mile if you happen to have artillery) it becomes irrelevant. A long front and countermarch technique (where front rows were firing and moving back while shooter from the back rows were loading rifles) made volley fire even more efficient. Blitzfeuer, a volley fired by 3 or sometimes even 4 rows of shooters simultaneously, famously used by Swedish infantry in 17th century could have stopped most attacks if timed well.

Firearms have also several other benefits over bows.

First, they are powerful. Very powerful. For example, mass-produced flintlock musket like 1768 British Short Land Service Musket with a 550-grain bullet (35 grams of lead) and standard charge (around 100 grain) had a muzzle energy in the ballpark of 1600-1700 J. That's roughly equal to an energy of modern 5.56 assault rifle (sure, the ballistics are vastly different, but that's another story). Due to this power, shooters were able to engage enemy over large distances and basically any direct hit eliminated the target from further battle. Please take not that during American War of Independence (or any European or American war in 18th century) armour was very scarce (usually limited to heavy cavalry) and most soldiers wore no protection whatsoever.

Second, the bow is more or less like a hand-to-hand weapons. It is only as strong its user is. In other words, the energy of the arrow is directly influenced by the strength of the archer. Weak person will be unable to draw the bow adequately, what means that archers needed to be strong (long-trained and well-fed). With a rifle shooter must be just strong enough to operate the device and withstand the recoil. This was even important as the time progressed and the size of the armies was rising while the number of strong people remained pretty constant.