The detail about schools - public schools in the US are locally funded in each School District, with some funding from state and federal government. Schools can and do bus children within Districts if individual schools are overcrowded. School Districts are obliged to accept and provide an appropriate education for every child whose parents register them. Local funding comes from property taxes.
Also, the detail about immigration - explain please the support for Trump in states where there are barely any immigrants or where immigrants find jobs and do not displace locals? Montana, Wyoming, Idaho, West Virginia, Maine, South Dakota, North Dakota, or states where immigrants themselves make up a large portion of the population - Florida, Texas...
Health services - what is that in the US context? There is private insurance that people entitled to work in the US get through work, private insurance bought under the terms of the ACA, and then there's Medicaid and Medicare, which are both government-provided healthcare benefits. Immigrants who do not have green cards are not entitled to healthcare on the public dime apart from maternity and baby and toddler healthcare services. Green card holders, who are entitled to work, are either employed or supported by a spouse, and either have health insurance provided by an employer or a spouse, have bought their own via the ACA, or are entitled to Medicaid (which is means tested) or Medicare (for those aged over 65). Healthcare providers are not creaking to meet need because of immigrants and displacing anyone's granny from her eye appointment.
And please explain why the states that supported Kamala Harris, and tend to support the Democratic candidate every time, are those where a huge number of immigrants end up - New York, Illinois, California.
Immigration in the US is an issue because of race. When Trump howls about "immigrants" he's talking in code and referring to brown and black people. This is the only aspect of US politics that has any similarity to the UK.