I run my piratebox on a TL-MR3040 so I can't say for certain on a Pi, but it looks like you have another service running that's listening on port 80:
[....] Starting lighttpd...:2015-10-30 21:49:13: (network.c.405) can't bind to port: 80 Address already in use
(warning).
As root run #netstat -tulpn to see what's sitting on port 80:
root@BetaPi:# netstat -tulpn
Active Internet connections (only servers)
Proto Recv-Q Send-Q Local Address Foreign Address State PID/Program name
tcp 0 0 0.0.0.0:3306 0.0.0.0:* LISTEN 5826/mysqld
tcp 0 0 0.0.0.0:80 0.0.0.0:* LISTEN 6702/apache2
tcp 0 0 0.0.0.0:22 0.0.0.0:* LISTEN 8132/sshd
In my example apache2 is currently listening to port 80. Find out what running on port 80 on your pi and use #service <PROGRAM NAME> stop to stop it and free up the port. That may be what's causing the dnsmasq failure too. Once the port is free you can try to run* again.
To keep the offending program from starting up when the pi restarts you can use #update-rc.d <SERVICE> disable to avoid conflicts the next time you reboot.
[....] Starting lighttpd...:2015-10-30 21:49:13: (network.c.405) can't bind to port: 80 Address already in use
(warning).
As root run #netstat -tulpn to see what's sitting on port 80:
root@BetaPi:# netstat -tulpn
Active Internet connections (only servers)
Proto Recv-Q Send-Q Local Address Foreign Address State PID/Program name
tcp 0 0 0.0.0.0:3306 0.0.0.0:* LISTEN 5826/mysqld
tcp 0 0 0.0.0.0:80 0.0.0.0:* LISTEN 6702/apache2
tcp 0 0 0.0.0.0:22 0.0.0.0:* LISTEN 8132/sshd
In my example apache2 is currently listening to port 80. Find out what running on port 80 on your pi and use #service <PROGRAM NAME> stop to stop it and free up the port. That may be what's causing the dnsmasq failure too. Once the port is free you can try to run* again.
To keep the offending program from starting up when the pi restarts you can use #update-rc.d <SERVICE> disable to avoid conflicts the next time you reboot.