Developmental delays

Hello everyone been a long time since I posted but hope someone can help. I wasn't sure where to post this really.
My Granddaughter who was 3 the end of may has a few developmental delays and was wondering if anyone who had experienced the same as hers could help.
She is lacking in social skills and does not like to play with anyone although she will now play with her key worker at pre-school a little more, if anyone goes to play with her (family included) she just looks at them, smiles and says bye and goes off somewhere else. Consequently she also has speech delays. She can understand questions and will follow instructions but she will not/cannot hold a conversation with anyone. She will only say a handful of words on her own but will copy things that you ask her to say. She knows all of her colours and will tell you what they are (without being asked). If you sing certain songs to her she listens and puts in the missing words (if that makes sense). She has seen a speech therapist twice and is under a paediatrician (although not been properly assessed by her yet).
Sorry for the long post, but if anyone can shed any light onto activities I can try to do with her, without upsetting her then please help a very worried Nana.
I have googled lots of things and looked at ICAN and we are looking into More Than Words but there is so much to read that it is very confusing.
Thank you for reading this.
Teacake2

There are a few things going on - speech delay and lack of social awareness seem to be the main ones.

It's hard without knowing the child but you know how to support language development - sing, read, talk and more talk ... and how to support children to make friends - one-to-one is usually easiest for children who struggle.

Hopefully she will get there with time. Have you followed up with the doctor? Made sure hearing is ok for example?

Missed you x

We have had an update last week about Ellie, her paediatrician has confirmed a diagnosis of Global Development Delay and very slight autism, although for the autism she only scores one on the list so they are reluctant to say she is autistic, and that is the social side of not wanting others to join in her little world when she is engrossed in playing. They are going to do some blood tests to see if there is anything genetic that is causing it, and are going to get her notes from the hospital from when she had suspected meningitis to see if it was a very mild case after all and that could have caused the problems. She has to see a educational psychologist so that she can get a statement (can't remember what it is called now) and so her pre-school can get extra funding for her and hopefully it will follow her to school etc for as long as she may need extra help.
I must say that she has come on leaps and bounds since being at pre-school since April although she missed quite a few sessions with illness and the older children who were leaving going out on trips and events.
She likes her key worker and after a bad start not wanting to go and not being any where near anyone she runs in shouting Amy Amy and likes to sit with her and doing activities, she still won't play with the others but will sit with them at snack time and watches them playing.
She was going to go to the school nursery in September but the headmaster can't get any funding for her support because it is only the nursery so she is staying at pre-school and I think if her improvement continues at the rate it has done she will probably be ready for school when she should go sept 2018.
Thanks for your advice Sarah, she likes listening to songs and will say some of the words that we leave out for her. She understands every thing that you say to her or ask her to do. She knows all of her colours and is starting to ask for things she wants, so I think there is a lot more hope for her now than before.
Teacake2

It can be useful to have a diagnosis as a gateway to further support - but a child must never be defined by their diagnosis - they will be amazing at some things and less good at others just like all children - they will learn in different ways and be stimulated by different things ...

All unique - all very special :D