COLD AS ICE: SOLUTION
1) Dead, she was killed Friday night. 2) Old Jho. 3) Jho used his freezer to disguise time of death.
Maketh Tua was a woman who would do anything to get what she wanted - and over the course of their affair, she wanted Valen Rudor. The way she saw to keep him was to quit their jobs and start a new life in Lothal, and Rudor would only agree to stay with her if she produced an impressive property for them to take over. Not one to back away from a challenge, Tua flipped through the possible seizures and found a perfect candidate: Old Jho's Inn, the most successful small business in Lothal and center of the community.
Despite the inn's success, Jho had fallen into debt after remodeling the kitchen and was beginning to default on his payments. On Friday night while the other guests were eating dinner Tua, wearing business attire and matching shoes, confronted him with the repossession paperwork in hand. Jho panicked and drowned her in the kitchen sink, creating the bruise across her chest from the sink basin.
Once the adrenaline wore off and he was left with a body Jho had to think fast. The ground was frozen solid so he couldn't bury the body, and once it was discovered the police wouldn't take long to figure out he was the only one who could have killed her. He had to create the illusion that Tua was still alive long enough to give himself an alibi, or even cover up the fact there had been a murder at all.
Jho slipped into the foyer, grabbed Tua's coat and boots from the communal coat rack and dressed her in them before putting the body in the freezer. He couldn't get back to Tua's room without the other guests noticing, so he hid her work shoes to dispose of later. Then he simply waited for Rudor to notice Tua was missing and made up the story about her going on a hike.
Late Sunday night when the search teams had turned in, Jho dumped the frozen body in the lake. He knew the medical examiner would be thrown off by the state of the body and mark time of death much later than it actually was, thus giving Jho an alibi for the "time" of the murder.
The killer's story crumbled when Kanan took a closer look at the autopsy report and realized Tua did not drown in the lake. In order for chlorinated water with no diatoms to get into her lungs she would have to drown in treated water, in town. She never left for a hike, and Old Jho was caught in a lie. This clue might have set Kanan on the right track, but it was Chopper who sealed the case. Remembering the dog's outburst earlier Kanan and Ezra searched the freezer. Deep inside were two strands of human hair and Maketh Tua's work shoes.