Is there any connection between the choice of characters for 九 and 丸?
「九」 and 「丸」 are not related. As @user3306356 points out, 「丸」 is probably related to 「夗」.

商朝甲骨文菁2.1合集6057西周金文作冊夨令簋集成4300戰國・晉金文東周左壺集成9640小篆九部說文解字今楷書　
「九」 depicts an arm showing the hand, a bent wrist, and elbow, indicating the original meaning elbow. This word is now written as 「肘」 (Baxter-Sagart OC: /*t-[k]&lt;r&gt;uʔ/).
The meaning nine (/*[k]uʔ/) for 「九」 is a phonetic loan.

「丸」 is derived from 「夗」.
「夗」 (/*[ʔ]o[r]ʔ/) was originally a picture of an animal or person curled up in a foetal position, extended to mean twisting and turning in bed and then crooked, winding (now written 「宛」).
「夗」 or its derivatives later started being used for different senses. 「丸」 (/*[ɢ]ʷˤar/) was corrupted from 「夗」 to specifically represent the sense curl up and roll &gt; ball, round object.
The glyph evolution and corruption process is as follows:
商朝甲骨文1799殷虛文字乙楷書　
西周金文能匋尊集成5984隸定文字　
西周金文仲義父鼎集成2542隸定文字　
小篆丸部說文解字
晉朝篆刻晉烏丸率善篆刻大字典
今楷書　

References:

季旭昇《說文新證》
小學堂
漢語多功能字庫
國學大師

郭沫若《甲骨文合集》
中國社會科學院考古研究所《殷周金文集成》


中國哲學書電子化計劃

宋・徐鉉等奉敕校定　漢・許慎《說文解字》