13:10-16 Does what Jesus says here that Satan had bound this woman for 18 years imply that Satan is the cause of all sickness and disease?

While Satan was directly involved in this woman's condition - a demon spirit (Jesus called it a spirit of infirmity), had taken possession of her and kept her bowed over for 18 years - he does not have to be directly involved to be the cause of all sickness and disease (cp Ac 10:38). This clearly teaches that everyone Jesus healed was oppressed by the devil (cp Mt 4:23-24; 8:8,13,16; 9:35; 12:9-15; 14:14, 35-36; 15:21-30; 19:2; 21:14; Mk 3:10-11; 5:25-29; 6:56; Lk 4:38-41; 5:12-15,17; 6:17-19; 7:1-10,21; 8:43-48; 9:10-11,37-42; 14:1-4; 17:11-17; 22:51; Jn 4:47).

The words heal, healed and healing in those scriptures all refer to people being healed, cured, and restored to bodily health.

Regardless of whether they were physically sick, diseased or possessed by demons, according to Ac 10:38 all the people that Jesus healed were oppressed by the devil. Oppressed means exercised dominion against, tyrannized (cp Lk 4:38-39). Peter's mother-in-law's fever is also mentioned in Mt 8:14-15 and Mk 1:30-31, but Luke is the only one who records that Jesus rebuked the fever in order to heal her. Rebuked means to admonish strongly, with urgency, authority.

Here it implies censure, strong condemnation, (as of demons). Jesus rebuked the fever here as He rebuked demons elsewhere in scripture (cp Mt 17:14-18, Mk 1:23-25, Lk 4:40-41). Although Lk 4:38-39 does not indicate that there were actual demons involved in Peter's mother-in-law's fever Jesus obviously saw it as the work of the devil and rebuked it accordingly (see also comments on Lk 4:38-39).