Does an American software company need to charge VAT for goods/ service rendered to a VAT registered company in EU?

Yes. According to new eu vat law, if you are a business in usa and sell a digital good or service to someone in eu, you are obliged to charge VAT and pay it to eu's vat agency. Engineering services are different, its a service rendered to each person per person, and does not fall under this law. you must check what kind of laws apply for that separately.

Perhaps. It will depend on the facts. Goods - if you are the importer of record then you may be required to charge local VAT dependent on the specific EU country. However if your customer is IOR then you should be OK unless the goods require installation which can complicate things. Services - I would think No here. Most B2B services are self assessed by the recipient (like Use Tax). I have seen some EU countries argue engineering services that relate to specific land or buildings being taxed where the land is.