1) ラーメン (Ramen)
This word comes from the Japanese adaptation of the Chinese word for "pulled noodles" = 拉面 =
"la1 mian4"
I think that the purpose of writing "Ramen" in Katakana is because the Japanese would like to identify that it is a foreign food. Indicating that it was initially from China.
It is essentially, a "loan word", that can be found widely used in Japan. Not only can this word be found on packaging but also on lanterns outside of Ramen shops.
According to this website:
Ramen became popular in the early 1900s, and was originally called "chuka-soba" but later on, during the 1950s, it was popularized once again, this time, becoming more wide spread.
According this this website:
"Ramen" was probably translated from "la mian" in Chinese. People believed that Chinese settlers in Japan influenced their food culture and therefore, allowed "ramen" noodles to evolve.
Ramen is a direct adaptation of a Chinese style dish; thus, to recognize and appreciate the word, it is written in katakana.
2) ブラシ (Brush)
Even though Japan already has a word for "brush" which is くし or 櫛, which means "comb," "brush" in Katakana can serve as other forms of "brushes" such as paintbrush, calligraphy brush, make up brush, etc.
A calligraphy brush in Japanese is called: ふで。
Therefore, as there are many different types of brushes, the general term "brush" can be used to group them under an umbrella category. In that case, it can be a relatively novel term that was borrowed as a "loan word".