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Can I say,

Last morning, Susan was having her lunch. After lunch / After having her lunch, she went to the kitchen to wash her hands with a bar of soap. She took off her ring and put it at the windowsill.

(i)She quickly rushed to the living room to answer the phone when the phone rang.

(ii) She quickly rushed into the living room when she heard the phone rang.

(iii) She quickly rushed in the living room while the phone rang.

She quickly rushed in the living room while she heard the phone rang.

She quickly rushed into the living room while ringing the phone.
Comments  
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You can use these:

Yesterday noon, Susan had her lunch. After lunch / After having her lunch, she went to the kitchen to wash her hands. She took off her ring and put it on the windowsill.

(i) When the phone rang, she quickly rushed to the living room to answer it.

(ii) She quickly rushed into the living room when she heard the phone ring.
(i) is the best, but it can be simplied as 'She quickly rushed to the living room to answer the phone when it rang.'

By the way, where have you read such expression as 'last morning'? Do you mean 'yesterday morning' or 'last Friday morning'?
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I'm not super experienced, but so far I can tell you it's
probably (ii) She quickly rushed into the living room to when she heard the phone ringing.
Because we're talking about a room, in this case a room you can go into.... and I think it should
be ringing instead of rang,however both are possible I suppose, at that particular moment in the
past it was ringing, you already using a lot of ed's and past simple, I don't know but ringing sounds more plausible:P
I mean little mistake

She quickly rushed into the living room, when she heard the phone ringing.
Can I say,

(a) As Susan was washing the hands, the phone rang.

(b) When /While Susan was washing the hands, the phone rang. At the same time, a crow flew into the kitchen.
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her hands rather than the hands, but otherwise ok.