Did the Companions directly propose to a girl for marriage?

The question can be interpreted in two ways:

First, that a woman proposing to herself was a common practice at that time. This is a clear error, as the Sunnah (definition) indicates that a woman is proposed to through her guardian (wali), and the Prophet, peace and blessings be upon him, ordered the segregation of men and women in places of worship and on the streets.

Second, that the intention is the occurrence of individual incidents where a man proposed to a woman without her guardian. This is permissible out of necessity and with legitimate Islamic controls: that the conversation is limited to what is necessary, without seclusion (khalwa (definition)) or temptation (fitnah), that it is not a result of prior arrangements, and that it is conducted in a proper manner without softness in speech. An example of this is a suitor addressing a woman who has no family.