<T05> - <T012> 9.5.3

9.5.3 Yellow and Red Card Rules
<T05> The Head Referee may assign a YELLOW CARD as a warning of egregious ROBOT or team member behavior at the ARENA. A YELLOW CARD will be indicated by the Head Referee standing in front of the TEAM’S PLAYER STATION and holding a yellow card in the air after the completion of the MATCH. In the first MATCH that a TEAM receives a YELLOW CARD, it acts as a warning.
<T06> Once a TEAM receives a YELLOW CARD, its team number will be colored yellow on the audience screen at the beginning of all subsequent MATCHES as a reminder to the team, the referees, and the audience that they have been issued a YELLOW CARD.
<T07> A TEAM will be issued a RED CARD (disqualification) in any subsequent MATCH that they receive an additional YELLOW CARD. This will occur after the completion of the MATCH. A RED CARD will be indicated by the Head Referee standing in front of the TEAM’S PLAYER STATION and holding a yellow card and red card in the air simultaneously. The TEAM will still carry their YELLOW CARD into subsequent matches.
<T08> If the behavior is particularly egregious, a RED CARD may be issued without being preceded by a YELLOW CARD, at the Head Referee’s discretion. The TEAM will still carry a YELLOW CARD into subsequent matches.
<T09> YELLOW CARDS do not carry forward between qualification matches and elimination matches. All TEAMS move into the elimination matches with a clean slate.
<T10> If a TEAM is disqualified during a MATCH for a reason other than receiving an additional YELLOW CARD, they will receive a RED CARD. This will occur after the completion of a MATCH and will be indicated by the Head Referee standing in front of the TEAM’S PLAYER STATION and holding a red card in the air.
<T11> During the qualification matches, a TEAM that receives a RED CARD will receive zero seeding points and zero coopertition bonus. The rest of the TEAMS in their ALLIANCE will still receive the earned seeding points and coopertition bonus.
<T12> During the elimination matches, a TEAM receiving a RED CARD will cause the disqualification of their entire ALLIANCE for that MATCH.

Can anyone clarify this? Do Yellow Cards really stay with you through the entire qualifying competition?

you posted it yourself
<T06> Once a TEAM receives a YELLOW CARD, its team number will be colored yellow on the audience screen at the beginning of all subsequent MATCHES as a reminder to the team, the referees, and the audience that they have been issued a YELLOW CARD.

Yellow cards only reset between qualification and elimination rounds.

Yellow cards carry through qualification matches, and are cleared before elimination matches. There is no change from last year. Notice <T07> that every subsequent yellow card results in a red card.

Is it just me, or are there more ways to get a yellow card this year?

seems to be more ways to get yellow cards as well as more ways to get red cards (meaning that there are actually multiple red card conditions in the manual this year).